Question

1. Which of these equations represents a line passing through (5.3) and (-5, -3)?

Answer 1

Answer:

The equation of the line is 5y-3x=0.

Explanation:

We are given two points: (x1,y1)=(5, 3) and (x2,y2)=(-5, -3)

Thus, we use the two-point form below to find the equation of the line.

$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$

Substituting the points gives:

$\begin{gathered} \frac{y-3}{x-5}=\frac{-3-3}{-5-5} \\ \frac{y-3}{x-5}=\frac{-6}{-10} \\ \frac{y-3}{x-5}=\frac{3}{5} \end{gathered}$

Next, simplify:

$\begin{gathered} 5(y-3)=3(x-5) \\ 5y-15=3x-15 \\ 5y-3x=-15+15 \\ 5y-3x=0 \end{gathered}$

The equation of the line is 5y-3x=0.