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.

Answer 1

Answer:

Slope = $-\frac{3}{4}$

y-intercept = 2

Equation of the line 't': $y=-\frac{3}{4}x+2$

Step-by-step explanation:

Slope of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is represented by,

Slope 'm' = $\frac{y_2-y_1}{x_2-x_1}$

Since line 't' is passing through two points (0, 2) and (8, -4),

Slope of the line 't' = $\frac{2+4}{0-8}$

                           m = $-\frac{6}{8}$

                           m = $-\frac{3}{4}$

Since y-intercept of a line is the value of 'y' for x = 0 [from point (0, 2) lying on this line]

Therefore, Y-intercept of line 't' = 2

Slope intercept of an equation is,

y = mx + b

where m = slope of the line

b = y-intercept

Therefore, equation of the line 't' will be,

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