Question

Which of the sets of equations represent the two lines graphed?

A) y = x + 2 and y = x - 4
B) y = x + 2 and y = -x - 4
C) y = -x + 2 and y = x - 4
D) y = x - 2 and y = -x - 4

Answer 1

B) y = x + 2 and y = -x - 4

Explanation:

Let the equation of a straight line with x-intercept 'a' and y-intercept 'b' be

`(x)/(a) + (y)/(b) = 1`

The line with positive slope has x-intercept a=-2 and y-intercept b=2.

Its equation is:

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

Multiply through by 2

`- x + y = 2`

Solve for y,

`\boxed {y = x + 2}`

For the line with a negative slope,

the x-intercept is a=-4 and the y-intercept is b=-4

Its equation is

`(x)/( - 4) + (y)/( - 4) = 1`

Multiply through by -4

`x + y = - 4`

Solve for y

`\boxed {y = - x - 4}`