Answer:
y = (3/4)x + 5 or x = y - (20/3) or 4y = 3x + 20
Step-by-step explanation:
To find the equation of a line that is perpendicular to the given line y + 7 = -4/3x and passes through the point (-8, -1), you can use the following steps:
First, determine the slope of the given line. The given line is in the slope-intercept form (y = mx + b), where m is the slope. In this case, the slope is -4/3.
The slope of a line perpendicular to the given line is the negative reciprocal of the slope of the given line. So, the slope of the perpendicular line is 3/4.
Use the point-slope form of the equation of a line to find the equation of the perpendicular line. The point-slope form is:
y - y1 = m(x - x1),
where (x1, y1) is the point through which the line passes, and m is the slope.
In this case, (x1, y1) = (-8, -1), and m = 3/4. So, the equation of the perpendicular line is:
y - (-1) = (3/4)(x - (-8)).
Simplify this equation:
y + 1 = (3/4)(x + 8).
To put it in standard form, you can multiply both sides of the equation by 4 to eliminate the fraction:
4(y + 1) = 3(x + 8).
Now, distribute on both sides:
4y + 4 = 3x + 24.
To isolate y, subtract 4 from both sides:
4y = 3x + 20.
Finally, divide by 4 to solve for y:
y = (3/4)x + 5.
So, the equation of the line perpendicular to y + 7 = -4/3x and passing through the point (-8, -1) is y = (3/4)x + 5.