3-4 Equations of Lines Name the slope and y-intercept of each equation. 1. y = ½ x + 4 m = ½ b = 4 2. y = 2 m = 0, b = 2 (horizontal line) 3. x = 5 m = undefined, no y-intercept (vertical line) 4. 4x – 3y = 12 Put into y = mx + b form y = 4/3 x – 4; m = 4/3, b = -4 Linear equation: Equation of a line Slope-intercept Form: y = mx + b m = slope of line b = y-intercept (where the line crosses the y-axis)

Graph using slope-intercept form Graph 2x – y = 4 First put it into the correct form. y = 2x – 4 What is m? What is b? m = 2 b = -4 Graph the y-intercept first. Then from that point use the slope to get your second point. Connect the dots.

Your Turn Graph the line –x + 3y = 9

Writing Equations Write an equation of the line that is parallel to the line y = -2x + 3 and passes through the point at (0,1). 1. What is the slope of the line given? -2 2. What is the slope of the line parallel to that? Plug in the slope, the x and y from the given point to find b. y = mx + b 1 = (-2)(0) + b 1 = 0 + b 1 = b Now plug b and m into slope-intercept form, leaving x and y as variables. y = -2x + 1 Use the point-slope form: y – y1 = m(x – x1) y – 1 = -2(x – 0) y – 1 = -2x

Point – Slope form of a line y – y1 = m(x – x1) m = slope x1 and y1 is the given point Write and equation in point-slope form with slope 4 that contains (-3,-6). Then simplify and write the equation in slope-intercept form. y + 6 = 4(x + 3) y = 4x + 6

Your Turn Write an equation of the line perpendicular to the graph of y = 3x + 4 that passes through the point (6,9). Slope = 3 so the perpendicular slope = -1/3 Point (6,9) so x1 = 6 and y1 = 9 Using point-slope form y – y1 = m(x – x1), write the equation of the line. y = -1/3x + 11

Practice Homework #21 p.169 13-31 odd, 33-34, 46-47