Question

Examine the linear graph to find the slope , y-intercept, and write the equation for this linear relationship ​

Answer 1

The slope of the line is:
`m=-(1)/(2)`

The y-intercept b = 3

The slope-intercept equation of the line is:
`y\:=\:-(1)/(3)x+3`

Explanation:

Taking two points from the given graph

(0, 3) and (6, 0)

Determining the slope m

The slope between (0, 3) and (6, 0) using the formula

`m=(y_2-y_1)/(x_2-x_1)`

where m is the slope between (x₁, y₁) and (x₂, y₂)

In our case,

• (x₁, y₁) = (0, 3)

• (x₂, y₂) = (6, 0)

now substitute (x₁, y₁) = (0, 3) and (x₂, y₂) = (6, 0) in the slope formula

`m=(y_2-y_1)/(x_2-x_1)`

`m=(0-3)/(6-0)`

`m=-(3)/(6)`

`m=-(1)/(2)`

Thus, the slope of the line is:
`m=-(1)/(2)`

Determining the y-intercept (b)

The slope-intercept form of the line equation is given by

`y = mx+b`

where

• 
  `m` is the slope

• 
  `b` is the y-intercept

From the graph, we can figure out the y-intercept by checking the value of y at x = 0.

If we closely check the graph, at x = 0, the value of y = 3

Therefore, the y-intercept b = 3

Slope-intercept Equation

We already know that the slope-intercept form of the line equation is

`y = mx+b`

substituting b = 3 and m = -1/2

`y\:=\:-(1)/(2)x+3`

Therefore, the slope-intercept equation of the line is:
`y\:=\:-(1)/(2)x+3`

The graph is also attached below.