5 7 PointSlope Form Objectives Graph a line

5 -7 Point-Slope Form Objectives Graph a line and write a linear equation using point-slope form. Write a linear equation given two points. Holt Algebra 1

5 -7 Point-Slope Form Example 1 A: Using Slope and a Point to Graph the line with the given slope that contains the given point. slope = 2; (3, 1) Step 1 Plot (3, 1). Step 2 Use the slope to move from (3, 1) to another point. 1 2 • Move 2 units up and 1 unit right and plot another point. Step 3 Draw the line connecting the two points. Holt Algebra 1 • (3, 1)

5 -7 Point-Slope Form Example 1 B: Using Slope and a Point to Graph the line with the given slope that contains the given point. slope = ; (– 2, 4) Step 1 Plot (– 2, 4). Step 2 Use the slope to move from ( – 2, 4) to another point. 4 3 (– 2, 4) • Move 3 units up and 4 units right and plot another point. Step 3 Draw the line connecting the two points. Holt Algebra 1 (2, 7) •

5 -7 Point-Slope Form Holt Algebra 1

5 -7 Point-Slope Form Example 2: Writing Linear Equations in Point-Slope Form Write an equation in point-slope form for the line with the given slope that contains the given point. C. A. B. Holt Algebra 1

5 -7 Point-Slope Form Check It Out! Example 2 Write an equation in point-slope form for the line with the given slope that contains the given point. a. b. slope = 0; (3, – 4) y – (– 4) = 0(x – 3) y + 4 = 0(x – 3) Holt Algebra 1

5 -7 Point-Slope Form Example 3: Writing Linear Equations in Slope. Intercept Form Write an equation in slope-intercept form for the line with slope 3 that contains (– 1, 4). Step 1 Write the equation in point-slope form: y – y 1 = m(x – x 1) y – 4 = 3[x – (– 1)] Step 2 Write the equation in slope-intercept form by solving for y. Rewrite subtraction of negative y – 4 = 3(x + 1) numbers as addition. y – 4 = 3 x + 3 Distribute 3 on the right side. +4 + 4 Add 4 to both sides. y = 3 x + 7 Holt Algebra 1

5 -7 Point-Slope Form Example 3 b: Writing Linear Equations in Slope. Intercept Form Write an equation in slope-intercept form for the line with slope -½ that contains (6, -2). Step 1 Write the equation in point-slope form: y – y 1 = m(x – x 1) y – (-2) = -½[x – (6)] Step 2 Write the equation in slope-intercept form by solving for y. y + 2 = -½(x - 6) y + 2 = -½x + 3 Distribute -½ on the right side. -2 -2 Subtract 2 from both sides. y = -½x + 1 Holt Algebra 1

5 -7 Point-Slope Form Example 4 A: Using Two Points to Write an Equation Write an equation in slope-intercept form for the line through the two points. (2, – 3) and (4, 1) Step 1 Find the slope. Step 2 Substitute the slope and one of the points into the point-slope form. y – y 1 = m(x – x 1) y – (– 3) = 2(x – 2) Holt Algebra 1 Choose (2, – 3).

5 -7 Point-Slope Form Example 4 A Continued Write an equation in slope-intercept form for the line through the two points. (2, – 3) and (4, 1) Step 3 Write the equation in slope-intercept form. y + 3 = 2(x – 2) y + 3 = 2 x – 4 – 3 y = 2 x – 7 Holt Algebra 1

5 -7 Point-Slope Form Example 4 B: Using Two Points to Write an Equation Write an equation in slope-intercept form for the line through the two points. (0, 1) and (– 2, 9) Step 1 Find the slope. Step 2 Substitute the slope and one of the points into the point-slope form. y – y 1 = m(x – x 1) y – 1 = – 4(x – 0) Choose (0, 1). Holt Algebra 1

5 -7 Point-Slope Form Example 4 B Continued Write an equation in slope-intercept form for the line through the two points. (0, 1) and (– 2, 9) Step 3 Write the equation in slope-intercept form. y – 1 = – 4(x – 0) y – 1 = – 4 x +1 +1 y = – 4 x + 1 Holt Algebra 1