Answer:
Option B is the correct option
[tex]\begin{gathered} y=\frac{3}{4}x+1 \\ \\ is\text{ the line parallel to the line that passes through the given points} \end{gathered}[/tex]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:
[tex]S=\frac{y_2-y_1}{x_2-x_1}[/tex]Here:
[tex]\begin{gathered} x_1=1 \\ y_1=7 \\ x_2=-3 \\ y_2=4 \end{gathered}[/tex]Using these, the slope is:
[tex]\begin{gathered} S=\frac{4-7}{-3-1} \\ \\ =\frac{-3}{-4} \\ \\ =\frac{3}{4} \end{gathered}[/tex]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.
