Question

How do you graph `3x-5y=15` using intercepts?

Answer 1

See a solution process below:

Explanation:

To find the intercepts, equate one variable to `0` and solve for the other variable:

y-intercept

Set `x` to `0` and solve for `y` giving:

`3x - 5y = 15` becomes:

`(3 * 0) - 5y = 15`

`0 - 5y = 15`

`-5y = 15`

`(-5y)/color(red)(-5) = 15/color(red)(-5)`

`(color(red)(cancel(color(black)(-5)))y)/cancel(color(red)(-5)) = -3`

`y = -3` or `(0, -3)`

x-intercept

Set `y` to `0` and solve for `x` giving:

`3x - 5y = 15` becomes:

`3x - (5 * 0) = 15`

`3x - 0 = 15`

`3x = 15`

`(3x)/color(red)(3) = 15/color(red)(3)`

`(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = 5`

`x = 5` or `(5, 0)`

Next. we can plot the two points on the grid:

graph{((x-5)^2+(y)^2-0.125)((x)^2+(y+3)^2-0.125)=0 [-20, 20, -10, 10]}

Then, draw a line through the two points:

graph{(3x - 5y -15)((x-5)^2+(y)^2-0.125)((x)^2+(y+3)^2-0.125)=0 [-20, 20, -10, 10]}

Answer 2

Draw a straight line through the intercept points as indicated below.

Explanation:

Note that the given equation: `3x-5y=15` is a linear (straight line) equation with:
`x`-intercept (value of `x` when `y=0`) of `x=5`
and
`y`-intercept (value of `y` when `x=0`) of `y=-3`

Therefore we have the two points:
`color(white)("XXX")(x_1,y_1)=(5,0) and (x_2,y_2)=(0,-3)`

Plotting these two points on the Cartesian plane and drawing a straight line through them should give a graph that looks like: