Question

How do you find the slope and intercept to graph `y = 5x - 9`?

Answer 1

Looking at the `m` and `c` values of the equation.

Explanation:

General Form of a Straight Line Equation
The general form of an equation for a straight line is `y=mx+c` In your case `m=5` and `c=-9`

The Gradient or 'Slope'
`m` tells us the gradient or 'slope'. In your case this is 5, which means for every one coordinate you move along on the `x` axis, your line will move up 5 coordinates in the `y` axis.

The `y` Intercept
As for the `y` intercept, this is given by the value of `c`. In your case this is -9. Since we know that `x=0` on the `y` axis then we know -9 is reffering to the `y` coordinate. This means the `y` intercept is at the coordinate `(0,-9)`

The `x` Intercept
If you want to figure out the `x` intercept as well then follow the method below.

On the `x` axis we know that `y=0` we can put this into our equation and rearrange to find the value for `x` at this point.

`0=5x-9`
`9 = 5x` (Add 9 to both sides)
`9/5 =x` (Divide by 5 on both sides)

We know know `x = 9/5` or `x=1.8`

So the `x` intercept is at the point `(1.8,0)`

This should be enough information to draw the graph!

Answer 2

See the explanation.

Explanation:

`y=5x-9` is in slope-intercept form for a linear equation, `y=mx+b`, where `m` is the slope and `b` is the y-intercept.

By definition, `5` is the slope or `(5/1)`, and the y-intercept is `-9`.

The y-intercept is the value of `y` when `x=0`.

`y=5(0)-9=-9`
The point is `(0,-9)`

The x-intercept is the value of `x` when `y=0`.

`0=5x-9`

Add `9` to both sides.

`9=5x`

Divide both sides by `5`.

`9/5=x`

Switch sides.

`x=9/5=1.8`
The point is `(9/5,0)`

You can plot the x and y-intercepts and draw a straight line through the two points.

graph{y=5x-9 [-14.49, 17.53, -11.41, 4.61]}