ACT Math - How to find x or y intercept

What is the and intercepts of the linear equation given by:
?

$(0,8), \left(-\frac{8}{7},0\right)$

$(0,-8),\left(\frac{8}{7},0\right)$

$\left(0,\frac{7}{8}\right),(8,0)$

Explanation

To find the and intercept of a linear equation, find the points where and are equal to zero.

To do this, plug in zero for either variable and then solve for the other.

$\0 = 7x +8 ewline y = 7*0 + 8$

this yields:

$(0,8), \left(-\frac{8}{7},0\right)$

What is the x-intercept of the following line?

y = –3_x_ + 12

1/4

–4

–1/4

Explanation

The x-intercept occurs when the y-coordinate = 0.

y = –3_x_ + 12

0 = –3_x_ + 12

3_x_ = 12

x = 12/3 = 4

What is the -intercept of the following linear equation:
?

Give your answer as an ordered pair.

$\left(\frac{5}{2}, 0\right)$

$\left(0, \frac{5}{2}\right)$

$\left(-\frac{5}{2},0\right)$

Explanation

The x-intercept is the value of the linear equation with y = 0 (this means the line will be on the x-axis when y is zero).

Thus we plug 0 in for y and solve for x.

$\0 = -2x + 5 \ ewline 2x = 5 \ ewline x = \frac{5}{2}$ .

Now put it in an ordered pair, remember y = 0:
$\left(\frac{5}{2}, 0\right)$

What are the y and x intercepts of the given equation, respectively?

y = 2x – 2

(0, –2), (1, 0)

(0, –2), (2, 0)

(0, 2), (2, 0)

(0, –2), (–2, 0)

(0, 0), (0, 0)

Explanation

The equation is already in slope-intercept form. The y-intercept is (0, –2). Plug in 0 for y and we get the x intercept of (1, 0)

Find the -intercept(s) for the following equation:

$(\frac{9}{2},0)$

Explanation

To find the intercepts, is set equal to . This yields:

And finally $x=\pm3$

It is important to realize that both and must be included because is also equal to . Finally, these are put into their point forms, and .

What is the and intercepts of the following linear equation:

$\left(\frac{3}{8},0\right)$

$\left(-\frac{3}{8},0\right)$

$\left(0,-\frac{8}{3}\right)$

Explanation

To find the and intercepts of an equation, set each variable to zero (one at a time) and solve for the other variable.
$\0 = -8x + 3 ewline -3 = -8x ewline \frac{3}{8} = x$

Next, set to zero:

$\y = -8(0) +3 ewline y = 3$
Now put these two sets of points into two ordered pairs:

$\left(\frac{3}{8},0\right)$

What is the $\dpi{100} \small x$ -coordinate of the point in the standard $\dpi{100} \small (x,y)$ coordinate plane at which the two lines $\dpi{100} \small y=4x+8$ and $\dpi{100} \small y=3x-7$ intersect?