Geometry - How to find x or y intercept

What is the y-intercept of the line with the equation ?

Explanation

You should recognize that the given equation is in the point-slope form.

In order to find the y-intercept, rearrange the equation into slope-intercept form, .

Since, , the y-intercept must be located at

Find the x-intercept of the line .

$(\frac{3}{2}, 0)$

$\left(\frac{3}{4}, 0\right)$

Explanation

Recall that an x-intercept occurs when the line crosses the x-axis. Thus, the y-coordinate of the x-intercept must be .

Plug in for the y-value.

The x-intercept is located at .

Find the y-intercept of the line .

$\left(0, -\frac{6}{5}\right)$

$\left(0, \frac{5}{6}\right)$

$\left(0, \frac{4}{5}\right)$

Explanation

Recall that at the y-intercept, the line crosses the y-axis. This means that at the y-intercept, the value of the x-coordinate is .

Plug in for into the equation to find the y-intercept.

$y=-\frac{6}{5}$

The y-intercept for this line is $\left(0, -\frac{6}{5}\right)$ .

What is the y-intercept of a line with the equation ?

Explanation

You should recognize that the given equation is in the point-slope form.

In order to find the y-intercept, rearrange the equation into slope-intercept form, .

Since, , the y-intercept must be located at

Find the y-intercept of the line .

$\left(0, -\frac{7}{3}\right)$

$\left(0, \frac{3}{7}\right)$

$\left(0, -\frac{5}{3}\right)$

Explanation

Recall that at the y-intercept, the line crosses the y-axis. This means that at the y-intercept, the value of the x-coordinate is .

Plug in for into the equation to find the y-intercept.

$y=-\frac{7}{3}$

The y-intercept for this line is $\left(0, -\frac{7}{3}\right)$ .

Find the x-intercept of the line .

Explanation

Recall that an x-intercept occurs when the line crosses the x-axis. Thus, the y-coordinate of the x-intercept must be .

Plug in for the y-value.

The x-intercept is located at .

Find the x-intercept(s) for the circle $\small (x-4)^2 + y^2 = 9$

$\small 1, 7$

$\small -1, 7$

The circle never intersects the x-axis

$\small -5, 5$

$\small 7$

Explanation

The x-intercepts of any curve are the x-values where the curve is intersecting the x-axis. This happens when y = 0. To figure out these x-values, plug in 0 for y in the original equation and solve for x:

$\small (x-4)^2 + 0^2 = 9$ adding 0 or 0 square doesn't change the value

$\small (x-4)^2 = 9$ take the square root of both sides

$\small x - 4 = \pm 3$ this means there are two different potential values for x, and we will have to solve for both. First:

add 4 to both sides

$\small x = 1$

Second: $\small x - 4 = 3$ again, add 4 to both sides

Our two answers are and .

Find the x-intercept for the line

$y = -\frac{1}{3} x + 5$ .

$(\frac{5}{3}, 0 )$

$(-\frac{5}{3},0)$

Explanation

To find the x-intercept, plug in 0 for y, since the x-axis is where y = 0

$0 = -\frac{1}{3} x + 5$ subtract 5 from both sides

$-5 = -\frac{1}{3}x$ multiply both sides by -3

The x-intercept is

Find the x-intercept for the line .

$(\frac{1}{3}, 0)$

$(\frac{2}{3},0)$

$(-\frac{1}{3},0)$

$(\frac{4}{3}, 0)$

Explanation

Start by putting the equation into form, where is the slope, and is the y-intercept.

$y=\frac{4}{3}x-\frac{4}{9}$

By definition, the x-intercept is where the line crosses the x-axis. As such, the y-coordinate of this point must be .

Plug in for in the equation for this line.

$0=\frac{4}{3}x-\frac{4}{9}$

Now, solve for .

$\frac{4}{3}x=\frac{4}9$

$x=\frac{1}{3}$

The x-intercept is found at $(\frac{1}{3}, 0)$ .

Give the -coordinate of the -intercept of the line of the equation

$5\frac{3}{8}$

$6\frac{1}{7}$

$-1\frac{1}{7}$

$-\frac{7}{8}$

Explanation

The -intercept of the graph of a function is the point at which it intersects the -axis. The -coordinate is 0, so the -coordinate can be found by substituting 0 for in the equation and solving for :