WeBWorK using host: https://webwork.pcc.edu, format: simple, seed: 1756, course: orcca

Decide whether $(5,-2)$ and $(-10,-7)$ are on the graph of the equation $y=-\frac{3}{5}x+1\text{.}$

At $(5,-2)\text{:}$

$y$	$=$	$-\frac{3}{5}x+1$
	$=$

This equation is and $(5,-2)$ is the graph of $y=-\frac{3}{5}x+1\text{.}$

At $(-10,-7)\text{:}$

$y$	$=$	$-\frac{3}{5}x+1$
	$=$

This equation is and $(-10,-7)$ is the graph of $y=-\frac{3}{5}x+1\text{.}$

Solution

If the point $(5,-2)$ is on $y=-\frac{3}{5}x+1\text{,}$ once we substitute $x=5$ and $y=-2$ into the line’s equation, the equation should be true. Let’s try:

$\begin{aligned} y\amp=-\frac{3}{5}x+1\\ -2\amp\stackrel{?}{=}-\frac{3}{5}(5)+1\\ -2\amp\stackrel{\checkmark}{=} -3+1 \end{aligned}$

Because this last equation is true, we can definitively say that $(5,-2)$ is on the graph of $y=-\frac{3}{5}x+1\text{.}$

However, if we substitute $x=-10$ and $y=-7$ into the equation, it leads to $-7=7\text{,}$ which is false. This definitively tells us that $(-10,-7)$ is not on the graph.