What is the slope-intercept form of the equation of the line that passes through the points (9, 5) and (4, 1) ?

y=4/5x−11/5

y=4/5x−4/5

y=4/5x+2/5

y=4/5x+41/5

y = 4x/5 + 4/5

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 = 1

y1 = 5

x2 = 4

x1 = 9

Slope, m = (1 - 5)/(4 - 9) = - 4/-5 = 4/5

To determine intercept c, we would substitute m = 4/5, x = 4 and y = 1 into y = mx + c. It becomes

1 = 4/5 × 4 + c

1 = 1/5 + c

c = 1 - 1/5 = 4/5

The equation becomes

y = 4x/5 + 4/5

y = (4/5)x - 11/5

Step-by-step explanation:

Slope: (5 - 1)/(9 - 4) = 4/5

y = (4/5)x + c

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

c = 1 - 16/5

c = -11/5

y = (4/5)x - 11/5

both equations and proportions are better.