Objectives Graph a line and write a linear equation using point-slope form. Write a linear equation given two points.

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

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

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. A. B. C.

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)

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 – y1 = m(x – x1) y – 4 = 3[x – (–1)] Step 2 Write the equation in slope-intercept form by solving for y. Rewrite subtraction of negative numbers as addition. y – 4 = 3(x + 1) y – 4 = 3x + 3 Distribute 3 on the right side. + 4 + 4 Add 4 to both sides. y = 3x + 7

Example 3b: 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 – y1 = m(x – x1) 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

Example 4A: 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 – y1 = m(x – x1) y – (–3) = 2(x – 2) Choose (2, –3).

Example 4A 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 = 2x – 4 –3 –3 y = 2x – 7

Example 4B: 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 – y1 = m(x – x1) y – 1 = –4(x – 0) Choose (0, 1).

Example 4B 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 = –4x + 1 +1 y = –4x + 1