Question

Which equation represents the line through (4, -6) and (0, 2)?

Answer 1

Answer:

y = - 2x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m =

with (x₁, y₁ ) = (4, - 6) and (x₂, y₂ ) = (0, 2 )

m =  =  =  = - 2

The line crosses the x- axis at (0, 2 ) ⇒ c = 2

y = - 2x + 2 ← equation of line

Answer 2

Answer:

$y=-2x+2$

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when x=0).

1) Determine the slope (m)

$m=\displaystyle\frac{y_2-y_1}{x_2-x_1}$ where two points that fall on the line are $(x_1,y_1)$ and $(x_2,y_2)$

Plug in the given points (4, -6) and (0, 2):

$m=\displaystyle\frac{-6-2}{4-0}\\\\m=\displaystyle\frac{-8}{4}\\\\m=-2$

Therefore, the slope of the line is -2. Plug this into $y=mx+b$:

$y=-2x+b$

2) Determine the y-intercept (b)

The y-intercept occurs when x=0. We are given that (0,2) falls on the line, so therefore, 2 is the y-intercept. Plug this into $y=-2x+b$:

$y=-2x+2$

I hope this helps!