Answer:
The equation a parallel line will be:
[tex]y=\frac{4}{3}x-9[/tex]
Hence, option B is correct.
Step-by-step explanation:
Given the equation
[tex]8x-6y=7[/tex]
Writing the line into the slope-intercept form
[tex]y = mx+b[/tex]
where m is the slope and b is the y-intercept
so
[tex]8x-6y=7[/tex]
[tex]6y\:=\:8x-7[/tex]
Dividing both sides by 6
[tex]y=\frac{4}{3}x-\frac{7}{6}[/tex]
comparing with the slope-intercept form
Thus, the slope of the line = m = 4/3
We know that the parallel lines have the same slope.
Thus, the slope of the parallel line is also 4/3
Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line and (x₁, y₁) is the point
substituting the values m = 4/3 and the point (6, -1)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-\left(-1\right)=\frac{4}{3}\left(x-6\right)[/tex]
[tex]y+1=\frac{4}{3}\left(x-6\right)[/tex]
Subtract 1 from both sides
[tex]y+1-1=\frac{4}{3}\left(x-6\right)-1[/tex]
[tex]y=\frac{4}{3}x-9[/tex]
Thus, the equation a parallel line will be:
[tex]y=\frac{4}{3}x-9[/tex]
Hence, option B is correct.
