Question

How to graph: `y=-2/5x-2`?

Answer 1

Find two points on the line and draw a straight line through the points. See below.

Explanation:

The equation of a straight line in slope `(m)` and `y-`intercept `(c)` form is:

`y = mx+c`

In this example we are asked to graph: `y=-2/5x-2`

Which is a straight line with a slope of `-2/5` and `y-` intercept of `2`

The way to graph a straight line is to find two points on the line and draw a straight line through them. The line will actually extend infinitely in both directions - but we are limited by paper or screen size!

The simplest points to find are usually the `x-` and `y-`intercepts.

We already know the `y-`intecept is `-2`

The `x-`intercept occurs where `y=0`

I.e. where: `-2/5x-2 =0`

`2/5x = -2 -> x=-5`

Now we have our two points on the line: `(-5,0) and (0, -2)`

Hence we can draw the graph as below:

graph{(-y-2/5x-2)((x+5)^2+y^2-0.01)(x^2+(y+2)^2-0.01)=0 [-7.904, 6.144, -4.086, 2.93]}