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Find the X and Y Intercepts of a Line Using Algebra
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When the equation is written in the slope-intercept form (y=mx+b), we can find the y-intercept by looking at the equation. The value of b is the y-intercept. This is because the y-intercept is when the x value equals 0. When x = 0, mx = 0, so when x = 0, y = b.

To find the x-intercept, we set y = 0 and solve the equation for x. This is because when y = 0 the line crosses the x-axis.

When an equation is not in y = mx + b form, we can solve for the intercepts by plugging in 0 as needed and solving for the remaining variable.

Find the X and Y-Intercepts of a Line Using Algebra

To find y-intercept, set x = 0 and solve for y. The point will be (0, y).

To find x-intercept, set y = 0 and solve for x. The point will be (x, 0).

### Practice Problems

1. Find the y-intercept of the line: (
Solution
Solution:
$$y=-9$$
)
$${\text{y}}=-3{\text{x}}-9$$
2. Find the x-intercept of the line: (
Solution
Solution:
$$x=3$$
)
$${\text{y}}=-4{\text{x}}+12$$
3. Find the y-intercept of the line: (
Solution
Solution:
$$y=9$$
Details:
Written solution: To find y-intercept: set $${\color{Red}x = 0}$$ and solve for y. The point will be (0,y):

$$y − 9 = 3{\color{Red}x}$$

Substitute $${\color{Red}0}$$ in for $${\color{Red}x}$$:

$$y − 9 = 3 {\color{Red}(0)}$$

Multiply 3 times 0, which gives us:

$$y − 9 = {\color{Red}0}$$

Then add 9 to both sides to isolate y:

$$y − 9 {\color{Red}+9} = 0 {\color{Red}+9}$$

Which gives us:

$$y = 9$$

So the y-intercept is $$(0,9)$$.
)
$${\text{y}} − 9 = 3x$$
4. Find the x-intercept of the line: (
Solution
Solution:
$$x=6$$
)
$${\text{y}} + 12 = 2x$$
5. Find the y-intercept of the line: (
Solution
Solution:
$$y=-4$$
)
$${\text{x}}+6{\text{y}}=-24$$
6. Find the x-intercept of the line: (
Solution
Solution:
$$x=-4$$
Details:
To find x-intercept: set $${\color{Red}y = 0}$$ and solve for x. The point will be (x,0):

$$5{\text{x}}+4{\text{y}}=-20$$

Substitute $${\color{Red}0}$$ in for y:

$$5{\text{x}}+4{\color{Red}(0)}=-20$$

Multiply 4 times 0 which gives us:

$$5{\text{x}}+{\color{Red}0}=-20$$

$$\frac{1}{5}(5{\text{x}})$$ = $$5{\text{x}}=-20$$

Then multiply both sides by $$\dfrac{1}{5}$$ (or divide both sides by 5, both will give you the same solution):

$$-20\dfrac{1}{5}$$

Which gives us:

$${\text{x}}=-4$$

So they x-intercept is $$-4,0)$$
)
$$5{\text{x}}+4{\text{y}}=-20$$

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