Graph the line that passes through the point (2, 9) and has an y -intercept of 7. What is the x -intercept of this line?

Question

Quizplus · Accepted Answer

First we need to find the slope of the line using the given point and y-intercept.

Since the line passes through (2, 9), we can use the point-slope formula:

y - y1 = m(x - x1)

where (x1, y1) = (2, 9) and m is the slope.

Also, since the y-intercept is 7, another point on the line is (0, 7).

Using these two points:

(9 - 7)/(2 - 0) = m

m = 1

So the equation of the line is y - 9 = 1(x - 2), which simplifies to y = x + 7.

To find the x-intercept, we set y = 0:

0 = x + 7

x = -7

Therefore, the x-intercept is -7.

The correct choice is C.

Graph the Line That Passes Through the Point (2, 9)