Question

Determine the slope m, x-intercept, and y-intercept of the equation 5x – 2y = 10

Answer 1

Given the following equation:

`5x-2y=10`

We can find the y-intercept and the slope if we write it in slope-intercept form. To do this, we have to solve for 'y'. We would get the following:

`\begin{gathered} 5x-2y=10 \\ \Rightarrow-2y=10-5x \\ \Rightarrow y=(10-5x)/(-2)=(10)/(-2)-(5x)/(-2)=-5+(5)/(2)x \\ y=(5)/(2)x-5 \end{gathered}`

therefore, we have that the slope is m = 5/2 and the y-intercept is -5

To find the x-intercept, we can make y = 0 and solve for x to get the following:

`\begin{gathered} y=0 \\ \Rightarrow5x-2(0)=10 \\ \Rightarrow5x=10 \\ \Rightarrow x=(10)/(5)=2 \\ x=2 \end{gathered}`

therefore, the x-intercept is 2