Question

Which of the following equations correctly describes the graphed line?

y = -1/2x - 5


y = -1/2x + 5


y = 1/2x + 5


y = 1/2x - 5

Answer 1

Option C i.e. y = 1/2x + 5 is the correct option.

Explanation:

The slope-intercept form of the line equation

y = mx+b

where

• m is the slope

• b is the y-intercept

Given the points

A(4, 7)

B(-4, 3)

Determining the slope between A and B

• (x₁, y₁) = (4, 7)

• (x₂, y₂) = (-4, 3)

Using the formula

Slope = m = [y₂ - y₁] / [x₂ - x₁]

= [3 - 7] / [-4 - 4]

= -4 / -8

= 4/8

= 1/2

Thus, the slope of the line = m = 1/2

We know that the value of the y-intercept can be determined by setting x = 0 and determining the corresponding value of y.

From the graph, it is clear

at x = 0, y = 5

Thus, the y-intercept b = 5

now substituting m = 1/2 and b = 5 in the slope-intercept form

y = mx+b

y = 1/2x + 5

Therefore, the equation of line in the graph is:

y = 1/2x + 5

Thus, option C i.e. y = 1/2x + 5 is the correct option.