Question

How do you graph `y=-9x`?

Answer 1

See explanation.

Explanation:

Given:`y=-9x`

As the number in front of `x` (coefficient of `x`) is negative it means that the line slopes downward as you read left to right on the x-axis.

The graph crosses (intercepts) the x-axis at y=0
and crosses (intercepts) the y-axis as x=0.

Set y=0 giving: `" "0=-9x => x=0`
So x-intercept`->(x,y)=(0,0)`

Set x=0 giving: `" "y=-9xx0 =>y=0`
So y-intercept `->(x,y)=(0,0)`

This demonstrates that the strait line passes through the origin.
The origin is where the two axis cross. So this gives us the first point:

Let the first point be `P_1->(x_1,y_1)=(0,0)`

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All we need know is a second point. This may be determined by substituting any value you so chose into `x`

I chose `x->3`

So we have: `y=-9x" "->" "y=-(9)xx3 = -27`

Let the second point be`P_2->(x_2,y_2)=(3,-27)`
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Put a dot at each of these points and draw a strait line through them. Extend this line to the edge of the graph region.