Question

16. Which statement describes the graphs of y = -x + 3 and y = -x + 6?They intersect at the point (3,6).They are parallel. They are perpendicular.They intersect at the point (6,3).

Answer 1

Step 1

Check the slope of

y = -x + 3

and

y = -x + 6

`\begin{gathered} \text{The equation for a line is given as} \\ y=\text{ mx + c} \\ \text{where} \\ m=\text{ slope} \\ c=\text{ y-intercept} \\ \end{gathered}`

`\begin{gathered} \text{For y= -x +3} \\ m_1\text{ = -1} \\ \text{For y = -x + 6} \\ m_2=\text{ -1} \\ _{}_{}_{}_{}_{} \end{gathered}`
`\begin{gathered} \text{For parallel lines} \\ m_1=m_2 \end{gathered}`

Step 2

Plot the graph

Therefore, the statement that describes the graphs of both equations is that they are parallel.