Question

Elena wanted to find the slope and y-intercept of the graph 25x - 20y = 100. She decided to put the equation in slope-intercept form first. Here is her work:25x - 20y = 100 20y = 100 - 25x y = 5 - 5/4 xShe concluded that the slope is - 5/4 and the y-intercept is (0, 5).What was Elena's mistake?

Answer 1

Step 1

Write the function in slope-intercept form

`\begin{gathered} 25x-20y=100 \\ -20y=100-25x \\ (-20y)/(-20)=(100-25x)/(-20) \\ y=-5+(5)/(4)x \\ or \\ y=(5)/(4)x-5 \\ \text{Hence, the slope=}(5)/(4)\text{ and the y-intercept = (0,-5)} \end{gathered}`

Step 2

Decipher her mistake

`\begin{gathered} In\text{ her step 2, she made a mistake while moving terms} \\ \text{she had in step 1;} \\ 25x-20y=100 \\ \text{In step 2 she had;} \\ 20y=100-25x \\ \text{Instead of; -20y=100-25x} \\ \text{From this step onwards her solution was wrong} \end{gathered}`

Step 3

Conclude

When Elena moved 25x over to the right side so she could isolate y, she forget the negative sign before 20y and instead went ahead to write;

`\begin{gathered} 20y=100-25x \\ I\text{nstead of ;} \\ -20y=100-25x \\ \text{This was her mistake and its in her step 2} \end{gathered}`

Therefore,

`\begin{gathered} \text{The right slope =}(5)/(4) \\ \text{The right y-intercept=(0,-5)} \\ \text{Her slope and y-intercept are wrong} \end{gathered}`