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=(y_2-y_1)/(x_2-x_1)`

So, the slope(m) is:

`m=(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.