Question

What's the slope-intercept form of the equation of the line graphed in this figure?

A) y = –3∕5x + 1

B) y = –5∕ x – 1

C) y = 5∕3x + 1

D) y = 3∕5x + 1

Answer 1

Option D

Explanation:

Slope intercept form:

(-5, -2) ; x₁ = -5 & y₁ = -2

(5 , 4) ; x₂ = 5 & y₂ = 4

Plugin the points in the below mentioned formula and find the slope.

`\boxed{\bf slope =(y_2-y_1)/(x_2-x_1)}`

`\sf = (4-[-2])/(5-[-5])\\\\\\=(4+2)/(5+5)\\\\=(6)/(10)\\\\=(3)/(5)`

Equation of slope-intercept form: y =mx + b

Here, m is the slope and b is the y-intercept.

`\sf y = (3)/(5)x + b`

The line is passing through (5, 4). So, substitute the points in the equation and find the y-intercept.

`4 =(3)/(5)*5 + b\\\\\\4=3+b\\\\`

4 - 3 = b

b = 1

Slope intercept form of the equation:

`\sf y = (3)/(5)x + 1`