Question

Find x-intercept and y-intercept 5x-3y=-15

Answer 1

Answer with Explanation:

We have to find the x-intercept and the y-intercept, we can find the two by analyzing the standard equation of the line, which is as follows:

`y(x)=mx+b\Rightarrow(1)`

x-intercept and y-intercept for the equation (1) are as follows:

`\begin{gathered} b\Rightarrow\text{ y-intercept} \\ y(x)=0\Rightarrow\text{ x-intercept} \end{gathered}`

Writing the given equation into the standard form results in the following:

`\begin{gathered} 5x-3y=-15\Rightarrow y=(-5x-15)/(-3) \\ \therefore\Rightarrow \\ y(x)=(5)/(3)x+5 \end{gathered}`

Therefore the x and y-intercepts are as follows:

`\begin{gathered} \text{ y-intercept }\Rightarrow y=5 \\ x\text{ -Intercept:} \\ y(x)=0\Rightarrow y(x)=(5)/(3)x+5=0 \\ x=(-5\cdot3)/(5)=-3 \\ x=-3\Rightarrow\text{ x-intercept} \end{gathered}`

The following plot confirms the x-intercept and the y-intercept:

In conclusion x = -3 and y = 5 are x and y intercepts.