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

Slope =
`-(3)/(4)`

y-intercept = 2

Equation of the line 't':
`y=-(3)/(4)x+2`

Explanation:

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

Slope 'm' =
`(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' =
`(2+4)/(0-8)`

m =
`-(6)/(8)`

m =
`-(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=-(3)/(4)x+2`