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 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 = 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.