Question

What is the slope-intercept form of the equation of the line that passes through the points (−3, 2) and (1, 5) ?

Answer 1

Answer:y = 3x/4 + 17/4

Step-by-step explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

From the information given,

y2 = 5

y1 = 2

x2 = 1

x1 = - 3

Slope, m = (5 - 2)/(1 - - 3) = 3/4

To dedetermine the intercept c, we would substitute m = 3/4, x = 1 and y = 5 into y = mx + c, it becomes

5 = 3/4 × 1 + c

5 = 3/4 + c

c = 5 - 3/4 = 17/4

The equation becomes

y = 3x/4 + 17/4

Answer 2

Answer:

y = (3/4)x + 17/4

Step-by-step explanation:

Slope: (5 - 2)/(1 - -3) = 3/4

y = (3/4)x + c

5 = (3/4)(1) + c

c = 5 - 3/4

c = 17/4

y = (3/4)x + 17/4