Question

How do you graph `y=-5x+10` using intercepts?

Answer 1

See a solution process below:

Explanation:

First, find the `y`-intercept by setting `x` to `0` and calculating `y`:

y-intercept:

`y = (-5 * 0) + 10`

`y = 0 + 10`

`y = 10` or `(0, 10)`

Next, find the `x`-intercept by setting `y` to `0` and solving for `x`:

x-intercept:

`0 = -5x + 10`

`0 - color(red)(10) = -5x + 10 - color(red)(10)`

`-10 = -5x + 0`

`-10 = -5x`

`(-10)/color(red)(-5) = (-5x)/color(red)(-5)`

`2 = (color(red)(cancel(color(black)(-5)))x)/cancel(color(red)(-5))`

`2 = x`

`x = 2` or `(2, 0)`

We can next graph the two points on the coordinate plane:

graph{(x^2+(y-10)^2-0.125)((x-2)^2+y^2-0.125)=0 [-25, 25, -12.5, 12.5]}

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

graph{(y+5x-10)(x^2+(y-10)^2-0.125)((x-2)^2+y^2-0.125)=0 [-25, 25, -12.5, 12.5]}