Question

How do you graph `y = -5x + 2` using the slope and intercept?

Answer 1

`ul("Full explanation given using first principles.")`
The calculations become quite fast once you get used to them and start using shortcuts.

Explanation:

compare to the standardised form of `y=mx+c`

Where m is the gradient (slope)

This is the amount of up or down for a given amount along

The y-intercept is where `x=0` which is the value of `c`
The x-intercept is where `y=0`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine the gradient")`

Directly comparing `y=-5x+2` to the above we have:

Gradient (slope)`=m=-5`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine the y intercept")`

`y_("intercept") " is at " x=0 " "->y=-5(0)+2" "=" "2" "=" "c`

Full coordinate for `y_("intercept")->(x,y) = (0,2)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine the x intercept")`

`x_("intercept")" is at "y=0`

`=>" "y=-5x+2" " ->" "color(green)( 0=-5x+2)`

Add `color(red)( 5x)` to both sides

`color(green)(0color(red)( +5x)=-5xcolor(red)( +5x)+2)`

`5x=0+2`

`color(green)(5x=2)`

Divide both sides by `color(red)(5)`

`color(green)(5/(color(red)(5))x=2/(color(red)(5)))`

`x_("intercept")=2/5`

Full coordinate for `x_("intercept")->(x,y) = (2/5,0)`