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

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

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

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

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

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 +24 +24 Solve for b. Since 24 is subtracted to b, add 24 to both sides to undo the subtraction.

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

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.

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.

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

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

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

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.

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.

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.

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.

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.

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.

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

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

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

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.

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

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

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