Question

How do you graph the equation `-4x+1/2y=-1`?

Answer 1

Find the intersections of this line with the axes and draw the line through them.

Explanation:

Given:

`-4x+1/2y=-1`

Note that this is a linear equation - all of the terms are of degree at most `1`. Hence its graph is a straight line.

Setting `x=0` or covering up the term in `x`, we get the equation:

`1/2y = -1`

Multiplying both sides by `2`, we find:

`y = -2`

Hence the intersection with the `y` axis is at the point `(0, -2)`.

Setting `y=0` or covering up the term in `y`, we get the equation:

`-4x=-1`

Dividing both sides by `-4`, we find:

`x = 1/4`

Hence the intersection with the `x` axis is at the point `(1/4, 0)`

Now we can draw the graph by drawing a line through the two intersections we have found:
graph{(4x^2+(y+2)^2-0.003)(4(x-1/4)^2+y^2-0.003)(-4x+1/2y+1) = 0 [-2.51, 2.5, -2.8, 2.4]}