Question

In slope-intercept form, what is the equation of the line passing through the points (3, 17) and (7, 25)?

A.y = −2x + 23
B. y = 2x − 11
C. y = −3x + 26
D. y = 2x + 11

Answer 1

Answer: D. y = 2x + 11

Explanation:

The slope-intercept form is:

`y=mx+b`

where m is the slope of the line and b is the y-intercept.

To find the slope:

`m=(y_(2)-y_(1))/(x_(2)-x_(1)) =(25-17)/(7-3)=(8)/(4)=2`

Then, the slope-intercept form so far is:
`y=2x+b`

Now, to find the y-intercept, you're going to choose one of the two points given and substitute it into the equation (the first coordinate into the x, and the second coordinate into the y), and then isolate the b. In this case, let's use the first point (3, 17):

`y=2x+b\\17=2(3)+b\\b=17-6\\b=11`

Substituting, you're left with the final slope-intercept form equation of the line passing through (3, 17) and (7, 25):

`y=2x+11`