Question

How do you graph `3x+4y=-10` using intercepts?

Answer 1

See a solution process below:

Explanation:

First, we will find the `x` intercept by solve the equation for `y =`:

`3x + (4 * 0) = -10`

`3x + 0 = -10`

`3x = -10`

`(3x)//color(red)(3) = -10/color(red)(3)`

`x = -10/3` or `(-10/3, 0)`

Next, we will find the `y` intercept by solve the equation for `x =`:

`(3 xx 0) + 4y = -10`

`0 + 4y = -10`

`4y = -10`

`(4y)//color(red)(4) = -10/color(red)(4)`

`y = -5/2` or `(0, -5/2)`

We can then plot the two intercepts on the coordinate plane:

graph{(x^2+(y+(5/2))^2-0.025)((x+(10/3))^2+y^2-0.025)=0 [-10, 10, -5, 5]}

Now, we can draw a straight line through the two points to graph the line:

graph{(3x + 4y + 10)(x^2+(y+(5/2))^2-0.025)((x+(10/3))^2+y^2-0.025)=0 [-10, 10, -5, 5]}