Question

-4x + 7 = 2y - 3
y-intercept:

x intercept:

Answer 1

x-intercept:
`\bigg((5)/(2), \:0\bigg)`

y-intercept:
`(0,\:5)`

Explanation:

To find the x-intercept, substitute in
`0` for
`y` and solve for
`x`.

`-4x + 7 = 2y - 3`

`-4x+7=2\left(\bold{0}\right)-3`

Simplify 2(0):
`-4x+7=2\cdot \:0-3`

Subtract 0 - 3 = -3:
`-4x+7=-3`

Subtract 7 from both sides:
`-4x+7-7=-3-7`

Simplify:
`-4x=-10`

Divide both sides by -4
`(-4x)/(-4)=(-10)/(-4)`

`\bold{x=(5)/(2)}`

To find the y-intercept, substitute in
`0` for
`x` and solve for
`y`.

`-4x + 7 = 2y - 3`

`-4(\bold{0})+7=2y-3`

Switch sides:
`y-3=-4\left(0\right)+7`

Simplify -4(0):
`2y-3=-0+7`

Add 3 to both sides:
`2y-3+3=7+3`

Simplify:
`2y=10`

Divide both sides by 2:
`(2y)/(2)=(10)/(2)`

`\bold{y=5}`