Question

How do you graph `y = 1/2x- 6` using the slope and intercept?

Answer 1

See explanation.

A lot of method detail given. The actual calculation is a lot faster than given once you are used to equations of this type.

Explanation:

Given: `y=1/2x-6`

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

`color(blue)("Teaching bit about gradient")`

Where `m->" gradient"->("change in y")/("change in x")`

Note that the gradient is consequential to reading left to write on the x-axis. This is important as it indicates if the graph is like 'going up a hill' or if it is like 'going down a hill' left to right.

Negative gradient is going down `y->" becomes less"`
Positive gradient is going up `y->" becomes greater"`

So we have `m=("change in y")/("change in x")->1/2`

As this is positive the graph 'goes up' reading left to right.

`m=("change in y")/("change in x")->1/2` means that for every change of 1 in the y-axis the x-axis changes by 2.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the question")`

`color(brown)("Determine the y-intercept")`

The plot crosses the y-axis at `x=0` so by substitution we have:

`y_("intercept")=1/2(0)-6`

`y_("intercept")=0-6`

`y_("intercept")=-6`

`y_("intercept")->(x,y)=(0,-6) color(green)(" Notice "-6" is the constant"`
`" "color(green)(darr)`
`" "y=mxcolor(green)(+c)`

`color(brown)("Determine the x-intercept")`

The plot crosses the x-axis at `y=0` so by substitution we have:

`0=1/2x_("intercept")-6`

Add 6 to both sides

`6=1/2x_("intercept")`

Multiply both sides by 2

`12=x_("intercept")`

`x_("intercept")->(x,y)=(12,0)`