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Holt McDougal Algebra 1

4-6

Slope-Intercept Form

Warm Up

Find each y-intercept.

1. y = 3x + 2 2. 5x – 3y = 12

Find each slope.

5. 4x + 2y = 10

6. 3x + 2 = 6y

Solve each equation for y.

4. 6x + 2y = 6

–4

–3

y = –2x + 5

Holt McDougal Algebra 1

4-6

Slope-Intercept Form

Write a linear equation in slope-intercept form.

Graph a line using slope-intercept form.

Objectives

Graph a line and write a linear equation usingpoint-slope form.

Write a linear equation given two points.

Holt McDougal Algebra 1

4-6

Slope-Intercept Form

Additional Example 1: Graphing by Using Slope and

y-intercept

Graph the line given the slope and y-intercept.

Step 1 The y-intercept is 4, so theline contains (0, 4). Plot (0, 4).

Step 3 Draw the line through the two points.

•

•

Run = 5

Rise = –2

Step 2 Slope =Count 2 units down and 5 unitsright from (0, 4) and plot anotherpoint.

; y intercept = 4

Slope =-

Holt McDougal Algebra 1

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Slope-Intercept Form

Any linear equation can be written in slope-interceptform by solving for y and simplifying. In this form,you can immediately see the slope and y-intercept.Also, you can quickly graph a line when the equationis written in slope-intercept form.

Holt McDougal Algebra 1

4-6

Slope-Intercept Form

Additional Example 2A: Writing Linear Equations inSlope-Intercept Form

Write the equation that describes the line inslope-intercept form.

slope = ; y-intercept = 4

y = mx + b

y = x + 4

Substitute the given values form and b.

Simply if necessary.

Holt McDougal Algebra 1

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Slope-Intercept Form

slope = –9; y-intercept =

y = mx + b

Substitute the given values form and b.

Simply if necessary.

Additional Example 2B: Writing Linear Equations inSlope-Intercept Form

Write the equation that describes the line inslope-intercept form.

y = –9x +

Holt McDougal Algebra 1

4-6

Slope-Intercept Form

Additional Example 2C: Writing Linear Equations inSlope-Intercept Form

Write the equation that describes the line inslope-intercept form.

Step 1 Find the y-intercept.The graph crosses the y-axisat (0, 3), so b = 3.

Step 2 Find the slope. Theline contains the points (–4, 1)and (–2, 2).

Holt McDougal Algebra 1

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Slope-Intercept Form

Additional Example 2C Continued

Write the equation that describes the line inslope-intercept form.

Use the slope formula.

Substitute (–4,1) for (x1 , y1)

and (–2, 2) for (x2 , y2) .

y = mx + b

Write the slope-intercept form.

Step 3 Write the equation.

Holt McDougal Algebra 1

4-6

Slope-Intercept Form

slope = 2; (3, 4) is on the line.

y = mx + b

Substitute 2 for m, 3 for x, and4 for y.

4 = 2(3) + b

Step 1 Find the y-intercept.

–2 = b

4 = 6 + b

–6 –6

Write the slope-intercept form.

Solve for b. Since 6 is added tob, subtract 6 from both sidesto undo the addition.

Additional Example 2D: Writing linear Equations inSlope-Intercept Form

Write the equation that describes the line inslope-intercept form.

Holt McDougal Algebra 1

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Slope-Intercept Form

Additional Example 2D Continued

Step 2 Write the equation.

y = mx + b

Write the slope-intercept form.

Substitute 2 for m, and –2 for b.

y = 2x + (–2)

y = 2x – 2

slope = 2; (3, 4) is on the line.

Write the equation that describes the line inslope-intercept form.

Holt McDougal Algebra 1

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Slope-Intercept Form

Additional Example 3A: Using Slope-Intercept Formto Graph

Write the equation in slope-intercept form.Then graph the line described by the equation.

y = 3x – 1

y = 3x – 1 is in the form y = mx + b

slope: m = 3 =

y-intercept: b = –1

Step 1 Plot (0, –1).

Step 2 Count 3 units up and 1unit right and plot another point.

Step 3 Draw the line connectingthe two points.

•

Holt McDougal Algebra 1

4-6

Slope-Intercept Form

Additional Example 3B: Using Slope-Intercept Formto Graph

Write the equation in slope-intercept form.Then graph the line described by the equation.

2y + 3x = 6

Step 1 Write the equation in slope-intercept formby solving for y.

2y + 3x = 6

–3x –3x

2y = –3x + 6

Subtract 3x from both sides.

Since y is multiplied by 2,divide both sides by 2.

Holt McDougal Algebra 1

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Slope-Intercept Form

Additional Example 3B Continued

Step 2 Graph the line.

slope: m =

y-intercept: b = 3

• Plot (0, 3).

• Count 3 units down and 2 units right and plotanother point.

• Draw the line connecting the two points.

•

Write the equation in slope-intercept form.Then graph the line described by the equation.

is in the formy = mx + b.

Holt McDougal Algebra 1

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Point-Slope Form

Holt McDougal Algebra 1

4-7

Point-Slope Form

Additional Example 1A: Writing Linear Equations inPoint-Slope Form

Write an equation in point slope form for the linewith the given slope that contains the given point.

Write the point-slope form.

y – y1 = m (x – x1)

Holt McDougal Algebra 1

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Point-Slope Form

Additional Example 1B: Writing Linear Equations inPoint-Slope Form

Write an equation in point slope form for the linewith the given slope that contains the given point.

slope = –4; (0, 3)

Write the point-slope form.

y – y1 = m(x – x1)

y – 3 = –4(x – 0)

Substitute –4 for m, 0 for x1and 3 for y1.

y – 3 = –4(x – 0)

Holt McDougal Algebra 1

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Point-Slope Form

slope = 1; (–1, –4)

Additional Example 1C: Writing Linear Equations inPoint-Slope Form

Write an equation in point slope form for the linewith the given slope that contains the given point.

Write the point-slope form.

y – (–4) = 1(x – (–1))

Substitute 1 for m, –1 for x1,and –4 for y1.

y + 4 = 1(x + 1)

Rewrite subtraction of negativenumbers as addition.

y – y1 = m(x – x1)

Holt McDougal Algebra 1

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Point-Slope Form

Additional Example 2A: Using Point-Slope Form toGraph

y – 1 = 2(x – 3)

Graph the line described by the equation.

y – 1 = 2(x – 3) is in theform y – y1= m(x – x1).

The line contains the point (3, 1).

Step 2 Count 2 units up and 1 unitright and plot another point.

Step 1 Plot (3, 1).

Step 3 Draw the line connecting the two points.

(1,3)

(2,5)

Holt McDougal Algebra 1

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Point-Slope Form

Graph the line described by the equation.

The line contains the point (–2, 4).

Step 2 Count 3 units up and 4 units rightand plot another point.

Step 1 Plot (–2, 4).

(-2,4)

(2,7)

Step 3 Draw the line connecting the two points.

Additional Example 2B: Using Point-Slope Form toGraph

y – 4 = (x – (–2)) is in the

form y – y1= m(x – x1).

slope: m =

Holt McDougal Algebra 1

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Point-Slope Form

Graph the line described by the equation.

y + 3 = 0(x – 4)

y – (–3) = 0(x – 4) is in theform y – y1= m(x – x1).

The line contains the point (4, –3).

Step 2 There slope is 0. Everyvalue of x will be at y = –3.

Step 1 Plot (4, –3).

slope: m = 0

Step 3 Draw the line connecting the points.

Additional Example 2C: Using Point-Slope Form toGraph

Holt McDougal Algebra 1

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Point-Slope Form

Write the equation that describes each line inslope-intercept form.

Additional Example 3A: Writing Linear Equations inSlope-Intercept Form

Slope = 3, (–1, 4) is on the line.

Step 1 Write the equation in point-slope form:

y – 4 = 3[x – (–1)]

Step 2 Write the equation in slope-intercept form bysolving for y.

y – 4 = 3(x + 1)

Rewrite subtraction of negativenumbers as addition.

Distribute 3 on the right side.

y – 4 = 3x + 3

+ 4 + 4

y = 3x + 7

Add 4 to both sides.

y – y1 = m(x – x1)

Holt McDougal Algebra 1

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Point-Slope Form

(2, –3) and (4, 1)

Step 1 Find the slope.

Step 2 Substitute the slope and one of the pointsinto the point-slope form.

Choose (2, –3).

y – y1 = m(x – x1)

y – (–3) = 2(x – 2)

Additional Example 3B: Writing Linear Equations inSlope-Intercept Form

Write the equation that describes the line inslope-intercept form.

Holt McDougal Algebra 1

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Point-Slope Form

Step 3 Write the equation in slope-intercept form.

y = 2x – 7

–3 –3

Additional Example 3B Continued

Write an equation in slope-intercept form forthe line through the two points.

(2, –3) and (4, 1)

y + 3 = 2(x – 2)

y + 3 = 2x – 4

Holt McDougal Algebra 1

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Point-Slope Form

Additional Example 3C: Writing Linear Equations inSlope-Intercept Form

Write the equation that describes the line inslope-intercept form.

Step 2 Find the slope.

Holt McDougal Algebra 1

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Point-Slope Form

Additional Example 3C Continued

Write the equation that describes the line inslope-intercept form.

Step 3 Write the equation in slope-intercept form.

y = mx + b

y = –4x + 1

Write the slope-intercept form.

Substitute –4 for m and 1 for b.

Holt McDougal Algebra 1

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Point-Slope Form

Additional Example 4: Using Two Points FindIntercepts

Write an equation in slope-intercept form forthe line through (10, –3) and (5, –2).

Step 1 Find the slope.

Step 2 Write the equation in slope-intercept form.

Write the point-slope form.

Subtract 3 from both sides.

Holt McDougal Algebra 1

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Point-Slope Form

Step 3 Find the intercepts.

x-intercept:

Replace ywith 0 andsolve forx.

The x-intercept is –5, and the y-intercept is –1.

Additional Example 4 Continued

y-intercept:

Use the slope-intercept form toindentify the y-intercept.

Holt McDougal Algebra 1

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Point-Slope Form

Homework

Section 4-6 and 4-7 in the workbook

Workbook page 223: 1 – 7

Workbook page 229: 1, 2, and 3