Question

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

Answer 1

Answer:

slope = 2 and y- intercept = 4

Step-by-step 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 = $\frac{4-0}{0+2}$ = $\frac{4}{2}$ = 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

Answer:

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

Step-by-step explanation:

The slope is defined as

$m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

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

$m=\frac{4-0}{0-(-2)}=\frac{4}{2}=2$

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).