Question

A system of equations consists of a line s of the equation y = x – 5 and a line t that passes through the points (0, 2) and (8, –4). Answer the questions about line t to write the equation. What is the slope of line t? What is the y-intercept of line t? What is the equation in slope-intercept form of line t?

Answer 1

Answer:

-0.75

2

y=-0.75x+2

Step-by-step explanation:

because e D g E n U i T y

Answer 2

Answer:

$\text{The slope of the line t:}\ m=-\dfrac{3}{4}\\\\\text{The y-intercept of the line t:}\ b=2\\\\\text{The equation of a line t in the slope-intercept form:}\ y=-\dfrac{3}{4}x+2$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept → (0, b)

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have two points (8, -4) and (0, 2) → b = 2.

Calculate the slope:

$m=\dfrac{2-(-4)}{0-8}=\dfrac{6}{-8}=-\dfrac{3}{4}$

Therefore the equation of a line t in the slope-intercept form is:

$y=-\dfrac{3}{4}x+2$