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Sagot :
The slope-intercept form for an equation of a line looks like this:
[tex]y=mx+b[/tex]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:
[tex]25x-20y=100[/tex]We can substract 25x from both sides:
[tex]\begin{gathered} 25x-20y-25x=100-25x \\ -20y=100-25x \end{gathered}[/tex]Here we can see Elena's mistake. Instead of the equation I just wrote she got:
[tex]20y=100-25x[/tex]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:
[tex]\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}[/tex]Which means that the slope is 5/4 and the y-intercept is (0,-5).
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