Question

Describe and correct the error in finding the intercepts of the graph of the equations.a) According to the image above, what is the mistake?b) How can you fix the mistake?

Answer 1

A)

In order to find the x-intercepts you need to find the values of x which make:

`y=0`

And in order to find the y-intercept you need to evaluate the function for:

`x=0,y(0)`

So, for the equation:

`\begin{gathered} 3x+12y=24 \\ \text{ Rewrite the equation as:} \\ y=2-(1)/(4)x \\ \text{The x-intercept is:} \\ y=0 \\ 2-(1)/(4)x=0 \\ 2=(1)/(4)x \\ x=8 \\ x-\text{intercept}=(8,0) \\ ----- \\ \text{The y-intercept is:} \\ y(0)=2-(1)/(4)(0)=2 \\ y-\text{intercept}=(0,2) \end{gathered}`

The mistake is replace y = 0 in order to find the x-intercept, you need to find the values of x which make the function equal to 0, not replace y for 0.

b.

`\begin{gathered} y=2-(1)/(4)x \\ \text{ Remember find the values of x which make y = 0} \\ y=0 \\ 2-(1)/(4)x=0 \\ \text{solve for x:} \\ 2=(1)/(4)x \\ x=8 \end{gathered}`