X and Y Intercepts. X and Y Intercepts Essential Questions How can x-intercepts and y-intercepts be...
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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 interceptThe 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 interceptThe 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 = -2x-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 = 4y intercept = 3x-intercept = 4
Example of Finding Interceptsy = 2x 2
y-intercept x =0In 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 = 00= 2x 2 2 = 2x 1 = xx-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.
ExampleWrite 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