Question

Which line is parallel to the line that passes through the points (1,7) and (-3, 4)? A.y=-3/4x-5 B.y=3/4x+1 C.y=4/3x-8 D. y=11/4x+3

Answer 1

Answer:

Option B is the correct option

`\begin{gathered} y=(3)/(4)x+1 \\ \\ is\text{ the line parallel to the line that passes through the given points} \end{gathered}`

Step-by-step explanation:

Given the points (1, 7) and (-3, 4), we want to find the line that is parallel to the line that passes through them.

Let us find the slope of the given line, using the formula:

`S=(y_2-y_1)/(x_2-x_1)`

Here:

`\begin{gathered} x_1=1 \\ y_1=7 \\ x_2=-3 \\ y_2=4 \end{gathered}`

Using these, the slope is:

`\begin{gathered} S=(4-7)/(-3-1) \\ \\ =(-3)/(-4) \\ \\ =(3)/(4) \end{gathered}`

The slope is 3/4.

Any other line that has a slope 3/4 would be parallel to the line that passes through the given points.