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**Warm Up Find the slope of the line containing each pair of points.**

(0, 2) and (3, 4) 2. (–2, 8) and (4, 2) 3. (3, 3) and (12, –15) –1 –2

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Homework Review (4-6) 4x – 3 3 -2x 2/5 10 3 4 -1 -1/3 x + 6 2/5x – 1

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Homework Review (4-6) y = -x +3 y =4/3x - 4 y = 5/2x - 5

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**Objectives Write a linear equation in slope-intercept form.**

Graph a line using slope-intercept form. Write a linear equation given two points.

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Questions of the Day Does the coefficient of x in a linear equation always equal the slope?

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**Slope-Intercept Form 4-6**

Holt McDougal Algebra 1 4-6 Slope-Intercept Form Example 4B: Writing linear Equations in Slope-Intercept Form (When Given the Slope and a point) A line has a slope of 8 and (-3, 1) is on the line. Write the equation that describes this line in slope-intercept form. Step 1 Find the y-intercept. y = mx + b Write the slope-intercept form. 1 = 8(−3) + b Substitute 8 for m, −3 for x, and 1 for y. 25 = b 1 = −24 + b Solve for b. Since 24 is subtracted to b, add 24 to both sides to undo the subtraction.

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**Slope-Intercept Form 4-6 Example 4B Continued**

Holt McDougal Algebra 1 4-6 Slope-Intercept Form Example 4B Continued A line has a slope of 8 and (-3, 1) is on the line. Write the equation that describes this line in slope-intercept form. Step 2 Write the equation. y = mx + b Write the slope-intercept form. y = 8x + 25 Substitute 8 for m, and 25 for b. y = 8x + 25

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**Slope-Intercept Form 4-6 Example 4C & 4D**

Holt McDougal Algebra 1 4-6 Slope-Intercept Form Example 4C & 4D Write the equation that describes this line in slope-intercept form. 4C: A line has a slope of 3 and (4, 2) is on the line. 4D: A line has a slope of 4 and (0, -7) is on the line.

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**Slope-Intercept Form 4-6**

Holt McDougal Algebra 1 4-6 Slope-Intercept Form Example 4C: Writing linear Equations in Slope-Intercept Form (When Given the Slope and a point) Write the equation that describes the line in slope-intercept form. slope = 3; (4, 2) is on the line. Step 1 Find the y-intercept. y = mx + b Write the slope-intercept form. 2 = 3(4) + b Substitute 3 for m, 4 for x, and 2 for y. –10 = b 2 = 12 + b –12 –12 Solve for b. Since 12 is added to b, subtract 12 from both sides to undo the addition.

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**Slope-Intercept Form 4-6 Example 4C Continued**

Holt McDougal Algebra 1 4-6 Slope-Intercept Form Example 4C Continued A line has a slope of 3 and (4, 2) is on the line. Write the equation that describes this line in slope-intercept form. Step 2 Write the equation. y = mx + b Write the slope-intercept form. y = 3x - 10 Substitute 3 for m, and -10 for b. y = 3x - 10

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**Slope-Intercept Form 4-6**

Holt McDougal Algebra 1 4-6 Slope-Intercept Form Example 4D: Writing linear Equations in Slope-Intercept Form (When Given the Slope and a point) Write the equation that describes the line in slope-intercept form. slope = 4; (0, -7) is on the line. Step 1 Find the y-intercept. y = mx + b Write the slope-intercept form. -7 = 4(0) + b Substitute 4 for m, 0 for x, and -7 for y. –7 = b -7 = 0 + b

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**Slope-Intercept Form 4-6 Example 4D Continued**

Holt McDougal Algebra 1 4-6 Slope-Intercept Form Example 4D Continued A line has a slope of 4 and (0, -7) is on the line. Write the equation that describes this line in slope-intercept form. Step 2 Write the equation. y = mx + b Write the slope-intercept form. y = 4x - 7 Substitute 4 for m, and -7 for b. y = 4x - 7

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**Additional Example 5A: Using Slope-Intercept Form to Graph**

Holt McDougal Algebra 1 4-6 Slope-Intercept Form Additional Example 5A: Using Slope-Intercept Form to 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 form by 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.

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**Additional Example 5A Continued**

Holt McDougal Algebra 1 4-6 Slope-Intercept Form Additional Example 5A Continued Write the equation in slope-intercept form. Then graph the line described by the equation. Step 2 Graph the line. is in the form y = mx + b. • slope: m = y-intercept: b = 3 • Plot (0, 3). • Count 3 units down and 2 units right and plot another point. • Draw the line connecting the two points.

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**Slope-Intercept Form 4-6 Check It Out! Example 5B**

Holt McDougal Algebra 1 4-6 Slope-Intercept Form Check It Out! Example 5B Write the equation in slope-intercept form. Then graph the line described by the equation. is in the form y = mx + b. • slope: • y-intercept: b = 0 Step 1 Plot (0, 0). Step 2 Count 2 units up and 3 units right and plot another point. Step 3 Draw the line connecting the two points.

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**Slope-Intercept Form 4-6 Check It Out! Example 5C**

Holt McDougal Algebra 1 4-6 Slope-Intercept Form Check It Out! Example 5C Write the equation in slope-intercept form. Then graph the line described by the equation. 6x + 2y = 10 Step 1 Write the equation in slope intercept form by solving for y. 6x + 2y = 10 –6x –6x 2y = –6x + 10 Subtract 6x from both sides. Since y is multiplied by 2, divide both sides by 2.

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**Check It Out! Example 5c Continued**

Holt McDougal Algebra 1 4-6 Slope-Intercept Form Check It Out! Example 5c Continued Write the equation in slope-intercept form. Then graph the line described by the equation. Step 2 Graph the line. • y = –3x + 5 is in the form y = mx + b. • slope: m = y-intercept: b = 5 • Plot (0, 5). • Count 3 units down and 1 unit right and plot another point. • Draw the line connecting the two points.

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**Slope-Intercept Form 4-6 Check It Out! Example 5D**

Holt McDougal Algebra 1 4-6 Slope-Intercept Form Check It Out! Example 5D Write the equation in slope-intercept form. Then graph the line described by the equation. y = –4 y = –4 is in the form y = mx + b. slope: m = 0 = = 0 y-intercept: b = –4 Step 1 Plot (0, –4). • Since the slope is 0, the line will be a horizontal at y = –4.

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Example 1A Write an equation in slope-intercept form for the line through the two points. (1, –2) and (3, 10) Step 1 Find the slope. Step 2 Substitute the slope and one of the points into the slope intercept form. y = mx + b –2 = 6(1) + b

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Example 1A Continued Write an equation in slope-intercept form for the line through the two points. (1, –2) and (3, 10) Step 3 Solve for the y-intercept (b). –2 = 6(1) + b –2 = 6 + b -8= b Step 4 Write the equation in slope-intercept form. y = 6x – 8

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**Example 1B: Using Two Points Find Intercepts**

Write an equation in slope-intercept form for the line through (10, –3) and (5, –2). Step 1 Find the slope. Step 2 Substitute the slope and one of the points into the slope intercept form. y = mx + b -2 = -1/5(5) + b

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Example 1B Continued Step 3 Solve for the y-intercept (b). -2 = -1/5(5) + b -2 = -1 + b -1 = + b Step 4 Write the equation in slope-intercept form.

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Check It Out! Example 1C Write an equation in slope-intercept form for the line through the two points. (2, 15) and (–4, –3) Step 1 Find the slope. Step 2 Substitute the slope and one of the points into the slope intercept form. y= mx + b 15 = 3(2) + b

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**Check It Out! Example 1C Continued**

Step 3 Solve for the y-intercept (b). 15 = 3(2) + b 15 = 6 + b 9 = b Step 4 Write the equation in slope-intercept form. y = 3x + 9

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**Complete Examples 1D, 1E and 1F as Homework**

Closure Complete Examples 1D, 1E and 1F as Homework

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