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

Jul 23, 2017

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

#### Explanation:

Given:

$- 4 x + \frac{1}{2} y = - 1$

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:

$\frac{1}{2} y = - 1$

Multiplying both sides by $2$, we find:

$y = - 2$

Hence the intersection with the $y$ axis is at the point $\left(0 , - 2\right)$.

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

$- 4 x = - 1$

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

$x = \frac{1}{4}$

Hence the intersection with the $x$ axis is at the point $\left(\frac{1}{4} , 0\right)$

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]}