Question

4. What is the slope-intercept equation of the line that goes through the points (3, 5) and (-1,13)? A. y = 2x-1 B. y=-2x+1 C. y = 1/2x + 3 1/2 D. y = –2x+11

Answer 1

We will find the slope(m) and y-intercept as follows:

*Slope(m)

We replace the values of the points given in the following expression:

$m=\frac{y_2-y_1}{x_2-x_1}$

So, the slope(m) is:

$m=\frac{13-5}{-1-3}\Rightarrow m=-2$

The slope equals -2.

*Y-intercept

We will use the slope and one of the points given to replace in the following expression to find the y-intercept:

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

We will use the point (3, 5) but we can use any point that belongs to the line, that is:

$y-5=-2(x-3)$

Now, we solve for y, that is:

$\Rightarrow y-5=-2x+6\Rightarrow y=-2x+11$

From this, we have that the y-intercept equals 11.