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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