Question

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

Answer 1

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

Step-by-step 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.

`(y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1)`

Substituting the points gives:

`\begin{gathered} (y-3)/(x-5)=(-3-3)/(-5-5) \\ (y-3)/(x-5)=(-6)/(-10) \\ (y-3)/(x-5)=(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.