Answer:
[tex]\large\boxed{y=-\dfrac{4}{3}x-6}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/te]x
m - slope
b - y-intercept
Parallel line have the same slope. Therefore the equation of the line parallel to given line is:
[tex]y=-\dfrac{4}{3}x+11\to m=-\dfrac{4}{3}\\\\y=-\dfrac{4}{3}x+b[/tex]
Put the coordinates of the given point (-6, 2) to the equation:
[tex]2=-\dfrac{4}{3\!\!\!\!\diagup_1}(-6\!\!\!\!\diagup^2)+b[/tex]
[tex]2=(4)(2)+b[/tex]
[tex]2=8+b[/tex] subtract 8 from both sides
[tex]-6=b\to b=-6[/tex]
Finally:
[tex]y=-\dfrac{4}{3}x-6[/tex]
Answer:
[tex]y = -\frac{4}{3}x -6[/tex]
Step-by-step explanation:
If two lines are parallel then they have the same slope.
The slope-intercept form of a line is as follows:
[tex]y = mx + b[/tex]
Where m is the slope of the line and b is the intersection with the y axis.
In this case we have the following line:
[tex]y = -\frac{4}{3}x + 11[/tex]
Note that the slope of the line is:
[tex]m=-\frac{4}{3}[/tex]
Therefore a line parallel to this line will have the same slope [tex]m=-\frac{4}{3}[/tex]
[tex]y = -\frac{4}{3}x + b[/tex]
To find the value of the constant b we substitute the point given in the equation of the line and solve for b. Because we know that this line goes through that point
[tex]2 = -\frac{4}{3}(-6) + b[/tex]
[tex]2 = 8 + b[/tex]
[tex]b=-6[/tex]
Finally the equation is:
[tex]y = -\frac{4}{3}x -6[/tex]
