Question

3. Han wanted to find the intercepts of the graph of the equation 10x + 4y = 20.He decided to put the equation in slope-intercept form first. Below is his work.He concluded that the x-intercept is (1/2, ) and the y-intercept is (0,5)10x + 4y = 204y = 20 – 10.3y=5 - 10.23a. What error did Han make?3b. What are the x- and y-intercepts of the line? Explain or show yourreasoning.

Answer 1

Given the equation:

`10x+4y=20`

The slope-intercept form will be as follows:

`\begin{gathered} 4y=20-10x\rightarrow(/4) \\ y=(20)/(4)-(10)/(4)x \\ \\ y=5-2.5x \end{gathered}`

3a. What error did Han make?

He didn't divide 10 by 4

3b. What are the x- and y-intercepts of the line?

First, we will find the y-intercept

so, put x = 0

y = 5 - 0 = 5

So, the point of y-intercept is (0, 5)

Second, we will find the x-intercept

So, put y = 0

So,

`\begin{gathered} 0=5-2.5x \\ 2.5x=5 \\ x=(5)/(2.5)=2 \end{gathered}`

So, the point of the x-intercept is (2, 0)