X and Y Intercepts

X and Y Intercepts Essential Questions How can x-intercepts and y-intercepts be determined? How can equations be graphed using intercepts?

Y intercept The y-intercept is the point where a line crosses the y axis. At this point the value of x is 0. To find the y-intercept, plug 0 in for x in the linear equation and solve for y. y = 3x - 6 (0, -6) y = 3(0) – 6 y = -6

X intercept The x-intercept is the point where a line crosses the x axis. At this point the value of y is 0. To find the x-intercept, plug 0 in for y in the linear equation and solve for y. y = 3x - 6 (2, 0) 0 = 3x – 6 +6 +6 6 = 3x 2 = x

Example of Finding Intercepts -16x + 8y = -16 y-intercept x = 0 -16(0) + 8y = -16 8y = -16 y = -2 x-intercept y = 0 -16x + 8(0) = -16 -16x = -16 x = 1 y-intercept = -2 x-intercept = 1

Example of Finding Intercepts 3x + 4y = 12 y-intercept x = 0 3(0) + 4y = 12 4y = 12 y = 3 x-intercept y = 0 3x + 4(0) = 12 3x = 12 x = 4 y –intercept = 3 x-intercept = 4

Example of Finding Intercepts y = 2x – 2 y-intercept x =0 In this case the equation is written in slope-intercept form (y = mx + b); therefore, the -2 is the “b” or y-intercept x-intercept y = 0 0= 2x – 2 2 = 2x 1 = x x-intercept = 1

Find the Equation of the LineGiven the x- and y - intercepts Write the intercepts as ordered pairs. The x-intercept 4 is the ordered pair (4, 0). The y-intercept -2 is the ordered pair (0, -2). Calculate the slope. Substitute the slope and the y-intercept (b) into the slope-intercept formula.

Example Write the equation of the line with x-intercept 3 and y-intercept 2. x-intercept 3 = (3, 0); y-intercept 2 = (0, 2) Slope: y = mx + b