X- and y-intercept notes
x- and y-intercepts
What is an x-intercept?
Where our line “graph” crosses the ‘x-axis’, anything on the x-axis has a y-coordinate of 0
So the x-intercept is the point ( x, 0) where x is on the x-axis.
What is a y-intercept?
Where our line “graph” crosses the ‘y-axis’, anything on the y-axis has a x-coordinate of 0
So the y-intercept is the point ( 0, y) where y is on the y-axis.
A. What are the x- and y-intercepts of the graph below?
Write you answer as an ordered pair.
x-intercept (-1, 0)
y-intercept (0, -3)
Find the x- and y-intercepts in order pair form for the following two graphs.
x-intercept (-1, 0) x-intercept (3, 0)
y-intercept (0, 1) y-intercept (0, 2)
B. Write the coordinates for the x- and y-intercepts for the following examples.
1. x-intercept is 4 2. y-intercept is 4 3. y-intercept is -1
(4, 0) (0, 4) (0, -1)
4. x-intercept is -3.5 5. x-intercept is 0 6. y-intercept is -3/4
(-3.5, 0) (0, 0) (0, - ¾ )
C. Graph the equation [pic] and then find the x- and y-intercepts. Use your calculator to find good points! Solve for y : y = -2/3x + 2
|x |y |
|-3 |4 |
|0 |2 |
|3 |0 |
| | |
x-int: (3, 0)
y-int: (0, 2)
|x |y |
|4 |9 |
|2 |5 |
|0 |1 |
|-.5 |0 |
Given the table below, what is the x-intercept and the y-intercept?
x- intercept: (0.5, 0)
y intercept: (0,1)
D. We can also find the intercepts using algebra rather than graphing.
To find the x-intercept: Set y = 0, then solve for x. Write as an ordered pair.
To find the y-intercept: Set x = 0, then solve for y. Write as an ordered pair.
Find the x- and y-intercepts for the following examples using algebra. Show all work!
1. [pic] to find the x-int, we plug 0 in for y to find the y-int, we plug 0 in for x
0 = x -7 y = 0 - 7
+7 +7 y = -7
7 = x
x-int: (7, 0) y-int: (0, -7)
2. [pic] to find the x-int, we plug 0 in for y to find the y-int, we plug 0 in for x
0 = 2/3(x) + 6 y = 2/3(0) + 6
-6 -6
(3/2)(-6) = 2/3(x) (3/2) y = 6
-9 = x
x-int: (-9, 0) y-int: (0, 6)
3. [pic] to find the x-int, we plug 0 in for y to find the y-int, we plug 0 in for x
3x – 5(0) = 10 3(0) – 5y = 10
3x = 10 -5y = 10
3 3 -5 -5
x = 10/3 y = -2
x-int: (10/3, 0) y-int: (0, -2)
4. -3x +9y = 12 to find the x-int, we plug 0 in for y to find the y-int, we plug 0 in for x
-3x + 9(0) = 12 -3(0) + 9y = 12
-3x = 12 9y = 12
-3 -3 9 9
x = -4 y = 4/3
x-int: (-4, 0) y-int: (0, 4/3)
-----------------------
(-1, 0)
(0, -3)
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