Question

Find the x- and y-intercepts of the graph of

5x – 4y = 30. State your answers as whole
numbers or as improper fractions in
simplest form.

Answer 1

Solving for the x- and y-intercepts of a Linear Equation

Answer:

`x`-intercept:
`6`

`y`-intercept:
`-(15)/(2)\\`

Explanation:

Given:

`5x -4y = 30`

`x`-intercepts is solved when
`y = 0`. In finding the
`x`-intercepts in the given equation, we must solve for the value of
`x` when
`y = 0`.

Solving for
`x` when
`y = 0`:

`5x -4y = 30 \\ 5x -4(0) = 30 \\ 5x = 30 \\ (5x)/(5) = (30)/(5) \\ x = 6`

So the
`x`-intercept is
`6`. If you are asked in ordered pair form, it is
`(6,0)`.

In finding the
`y`-intercepts in the given equation, we must solve for the value of
`y` when
`x = 0`.

Solving for
`y` when
`x = 0`:

`5x -4y = 30 \\ 5(0) -4y = 30 \\ -4y= 30 \\ (-4y)/(-4) = (30)/(-4) \\ y = -(15)/(2)`

So the
`y`-intercept is
`-(15)/(2)\\`. If you are asked in ordered pair form, it is
`(0,-(15)/(2))\\`.