Question

7. Elena wanted to find the slope and y-intercept of the graph of 25x – 20y = 100. Shedecided to put the equation in slope-intercept form first. Here is her work:-25x - 20y = 10020y = 100 - 25x5y = 5 - 2x-4She concluded that the slope isand the y-intercept is (0,5).a. What was Elena's mistake?b. What are the slope and y-intercept of the line? Explain or show your reasoning.

Answer 1

The slope-intercept form for an equation of a line looks like this:

$y=mx+b$

Where m is the slope and (0,b) the y-intercept. Let's take the equation given by the question, operate and write it in slope-intercept form and see which was Elena's mistake. So we have:

$25x-20y=100$

We can substract 25x from both sides:

$\begin{gathered} 25x-20y-25x=100-25x \\ -20y=100-25x \end{gathered}$

Here we can see Elena's mistake. Instead of the equation I just wrote she got:

$20y=100-25x$

This doesn't have the negative sign in 20y. This was her mistake and answer to part a.

Now let's continue, we can divide both sides by -20:

$\begin{gathered} -\frac{20y}{-20}=\frac{100-25x}{-20} \\ y=-\frac{100}{20}+\frac{25}{20}x \\ y=\frac{5}{4}x-5 \end{gathered}$

Which means that the slope is 5/4 and the y-intercept is (0,-5).