Question

through: (-4,-1) and ( -1,2) ?
(A) y=-x+3.
(B)y=4x+3
(X) y=5x+3
(E)y=x+3
(D)y=3x+1

Answer 1

Answer:

(E) $y=x+3$

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 the line crosses the y-axis).

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,-1) and ( -1,2):

$m=\displaystyle \frac{2-(-1)}{(-1)-(-4)}\\\\m=\displaystyle \frac{2+1}{-1+4}\\\\m=\displaystyle \frac{3}{3}\\\\m=1$

Therefore, the slope of the line is 1. Plug this into $y=mx+b$:

$y=1x+b\\y=x+b$

2) Determine the y-intercept (b)

$y=x+b$

Plug in one of the given points and solve for b:

$2=-1+b\\2+1=b\\3=b$

Therefore, the y-intercept of the line is 3. Plug this back into the original equation:

$y=x+3$

I hope this helps!