Question

The coordinate grid below shows the graphs of two lines: line z and line m.

Answer 1

Let us find the slope of each line

slope of line l

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ m=(5-1)/(3-(-3))=(4)/(6)=(2)/(3) \end{gathered}`

slope of line m

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ m=(2-(-4))/(6-(-3))=(6)/(9)=(2)/(3) \end{gathered}`

The slopes are the same therefore no one is greater than each other. let us find the y -intercept and x - intercept of each line if required.

y-intercept of line l is

`\begin{gathered} y=mx+b \\ 1=(2)/(3)(-3)+b \\ b=y-\text{intercept} \\ 1=-2+b \\ 1+2=b \\ b=3 \end{gathered}`

y-intercept of line m is

`\begin{gathered} y=mx+b \\ -4=(2)/(3)(-3)+b \\ -4=-2+b \\ -4+2=b \\ b=-2 \end{gathered}`

The y-intercept of line l is greater than the y-intercept of line m.

The answer is B. The x-intercept of line m is greater than the x-intercept of line l.

we can prove it is option B by making y = 0 below

`\begin{gathered} \text{ line l} \\ y=mx+b \\ 0=(2)/(3)x+3 \\ -3=(2)/(3)x \\ -9=2x \\ x=-(9)/(2) \\ \\ \text{ line m} \\ y=mx+b \\ 0=(2)/(3)x-2 \\ 2=(2)/(3)x \\ 6=2x \\ x=(6)/(2) \\ x=3 \end{gathered}`