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?

Accepted Solution

Answer:[tex]\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[/tex]Step-by-step explanation:The slope-intercept form of an equation of a line:[tex]y=mx+b[/tex]m - slopeb - y-intercept β†’ (0, b)The formula of a slope:[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]We have two points (8, -4) and (0, 2) β†’ b = 2.Calculate the slope:[tex]m=\dfrac{2-(-4)}{0-8}=\dfrac{6}{-8}=-\dfrac{3}{4}[/tex]Therefore the equation of a line t in the slope-intercept form is:[tex]y=-\dfrac{3}{4}x+2[/tex]