Question

6.

Write the equation of the line in slope-intercept form that has the following points: (4, 5) (-1, 2)

A. y = 3/5x + 1

B. y = -x + 1

C. y = -x + 13/5

D. y = 3/5x + 13/5

Answer 1

D. y = 3/5x + 13/5

Explanation:

The slope of the desired line is the ratio of the difference in y-values to the difference in x-values:

m = Δy/Δx = (2 -5)/(-1 -4) = -3/-5 = 3/5 . . . . . . eliminates choices B and C

The slope-intercept equation will then be ...

y = mx + b . . . . . . . generic slope-intercept form

y = 3/5x + b . . . . . . put in m; true for some b that puts the given points on the line

Using the first point, we have ...

5 = 3/5×4 + b

25/5 = 12/5 + b

13/5 = b . . . . . . . . . subtract 12/5

Then the equation is ...

y = 3/5x + 13/5

_____

You know as soon as you consider putting a point value in the equation ...

y = 3/5x + b

that the equation of choice A cannot work. That only leaves choice D.