Question

18. State the slope and y-intercept of each linear equations.

a. 6(x + y) = 3(x - y)
b. 2(x + y) = 5(y + 1)
c. 5x + 10y - 20 = 0

Answer 1

a. The slope is
`(-1)/(3)` and the y-intercept is 0

b. The slope is
`(2)/(3)` and the y-intercept is
`-(5)/(3)`

c. The slope is
`(-1)/(2)` and the y-intercept is 2

Explanation:

The easiest way to find the slope and y-intercept is to put each equation in the slope-intercept form

That is:

y = mx = c

where m is the slope and c is the y-intercept

Part a:

6(x+y) = 3(x-y)

2(x+y) = x-y

2x + 2y = x - y

3y = -x

`y = (-1)/(3)x`

Comparing this with the general formula, we can conclude that:

The slope is
`(-1)/(3)` and the y-intercept is 0

Part b:

2(x+y) = 5(y+1)

2x + 2y = 5y + 5

3y = 2x - 5

`y = (2)/(3)x - (5)/(3)`

Comparing this with general formula, we can conclude that:

The slope is
`(2)/(3)` and the y-intercept is
`-(5)/(3)`

Part c:

5x + 10y -20 = 0

10y = -5x + 20

`y = (-1)/(2) x+2`

Comparing this with the general formula, we can conclude that:

The slope is
`(-1)/(2)` and the y-intercept is 2

Hope this helps :)