Question

What are the intercepts of the equation `-3x+4y=-12`? How do you graph it?

Answer 1

Intercepts are `4` on `x`-axis and `-3` on `y`-axis

Explanation:

`x`-intercept is obtained by putting `y=0` in the equation and here we get `-3x=-12` or `x=(-12)/(-3)=4`

For `y`-intercept, we put `x=0` i.e. `4y=-12` or `y=-3`

Hence, intercepts are `4` on `x`-axis and `-3` on `y`-axis

hence line passes through `(4,0)` and `(0,-3)` and joining them gives us the graph.

graph{(-3x+4y+12)((x-4)^2+y^2-0.01)(x^2+(y+3)^2-0.01)=0 [-3.48, 6.52, -4.08, 0.92]}

Answer 2

`"see explanation"`

Explanation:

`"to find the intercepts, that is where the graph"`
`"crosses the x and y axes"`

`• " let x = 0, in the equation for y-intercept"`

`• " let y = 0, in the equation for x-intercept"`

`x=0rArr0+4y=-12rArry=-3larrcolor(red)"y-intercept"`

`y=0rArr-3x+0=-12rArrx=4larrcolor(red)"x-intercept"`

`"plot the points "(0,-3)" and (4,0)`

`"draw a straight line through them for graph"`
graph{(y-3/4x+3)((x-0)^2+(y+3)^2-0.04)((x-4)^2+(y-0)^2-0.04)=0 [-10, 10, -5, 5]}