Question

What is the slope, m, and y-intercept for the line that is plotted on the grid below?

Answer 1

slope = 2 and y- intercept = 4

Explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2,0) and (x₂, y₂ ) = (0, 4) ← 2 points on the line

m =
`(4-0)/(0+2)` =
`(4)/(2)` = 2

The y- intercept is the value of the y- coordinate where the line crosses the y- axis, that is

y- intercept = 4 or (0, 4) in coordinate form, thus

y = 2x + 4 ← equation in slope- intercept form

Answer 2

The slope of the line is 2 and the y-intercept is at (0,4).

Explanation:

The slope is defined as

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

Where we need two points on the line to use the slope formula.

The points we selected are
`(-2,0)` and
`(0,4)`. Replacing this points, we have

`m=(4-0)/(0-(-2))=(4)/(2)=2`

Now, we use one point, the slope and the point-slope formula to find the equation

`y-y_(1) =m(x-x_(1) )\\y-4=2(x-0)\\y=2x+4`

Where
`m=2` and
`b=4` which is the y-intercept.

Therefore, the slope of the line is 2 and the y-intercept is at (0,4).