Question

Hello! can anyone explain to me how to solve this problem step by step?

Answer 1

From the given graph, the coordinates of the four points are A(-4,-2), B(4,4), C(0,-3) and D(4,0).

Find the equation of the line joining A and B using the two point formula.

`\begin{gathered} y-(-2)=(4-(-2))/(4-(-4))(x_{}-(-4)) \\ y+2=(6)/(8)(x+4) \\ y=(3)/(4)x+(3)/(4)\cdot4-2 \\ y=(3)/(4)x+1 \end{gathered}`

Find the equation of the line joining C and D using the two point formula.

`\begin{gathered} (y-(-3))=(0-(-3))/(4-0)(x-0) \\ y+3=(3)/(4)x \\ y=(3)/(4)x-3 \end{gathered}`

The equation of the line is in the form y = mx+c, where m is the slope and c is the y-intercept.

Here:

Slope of the line joining A and B = 3/4

Slope of the line joining C and D = 3/4

So, the lines are parallel because their slopes are equal.