Question

a line with a slope of 9 passes through the point ( 1, 7). what is its equation in slope-intercept form?

Answer 1

To answer this question, we need to remember that the slope-intercept form of the line is of the form:

$y=mx+b$

Where:

1. m is the slope of the line, and

2. b is the y-intercept of the line (that is the point when x = 0).

Then, we have from the question that:

m = 9

And the point is (1, 7).

Therefore, using the point-slope form of the line, we can proceed as follows to find, finally, the slope-intercept form of that line:

$y-y_1=m(x-x_1)$

x1 = 1

y1 = 7

$y-7=9(x-1)\Rightarrow y-7=9x-9$

Then, add 7 to both sides of the equation to solve for y:

$y-7+7=9x-9+7\Rightarrow y=9x-2$

Therefore, the equation of the line in slope-intercept form is:

$y=9x-2$