Question

How do you graph `y=1/5x-3` by plotting points?

Answer 1

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Graphs are available for:
`color(blue)(f(x) = x, color(green)(f(x) = (1/5)*x and color(brown)(f(x)=[(1/5)*x]-3`
for easy comprehension.

Explanation:

`" "`
`color(green)("Step 1:"`

Examine the graph of `color(blue)(y=f(x)=x`

Slope-Intercept Form `y= mx+b`

This is of the form `y=1*x+0`, where `Slope(m)=1` and `"y-intercept"=0`

Remember that the Slope(m) is the constant ratio that compares the change in y values over the change in x values between any two points.

y-intercept is the coordinate point where the graph crosses the y-axis.

`color(green)("Step 2:"`

Examine the graph of `color(green)(y=f(x)=(1/5)*x`

This graph is also in Slope-Intercept Form : `y=mx+b`, where `Slope(m)=(1/5)` and y-intercept is `0`.

`color(green)("Step 3:"`

First we will create a data table for `x` and the corresponding `y` values:

Construct the graph using these data values.

Examine the graph of `color(brown)(y=f(x)=(1/5)*x-3`

The equation is of `y=mx+b` form:

`Slope(m)=1/5` and y-intercept `=(0,-3)`

Hope you find this solution useful.