Answer:
Equation of the line: 7x + 4y = -96
A = 7, B = 4, C = -96
Explanation:
Step 1: Find the slope of 7x + 4y = -83 by converting it to the slope-intercept form:
7x + 4y = -83 is in the standard form of a line, whose general equation is given by:
Ax + By = C
- The standard form is helpful when determining the x- and y-intercepts, but not the slope.
However, the slope-intercept form is perfect for determining the slope and its general equation is given by:
y = mx + b, where
- m is the slope,
- and b is the y-intercept:
Thus, we'll need to convert 7x + 4y - 83 to slope-intercept form by isolating y on the left-hand side of the equation:
(7x + 4y = -83) - 7x
(4y = -7x - 83) / 4
y = -7/4x - 83/4
Thus, the slope of 7x + 4y - 83 is -7/4.
Step 2: Find the y-intercept of the other line:
The reason we had to find the slope of 7x + 4y = -83 is because the slopes of parallel lines are equal, meaning that the slope of the other (unknown) line is also -7/4.
Since the other line passes through the points (-8, -10), we can find b, the y-intercept of the other line by plugging in -7/4 for m, (-8, -10) for (x, y) into the slope-intercept form:
First, we need to simplify on the right-hand side by multipling -7/4 and -8:
-10 = -7/4(-8) + b
-10 = 14 + b
Now we need to subtract 14 from both sides to solve for b, the y-intercept of the other line:
(-10 = 14 + b) - 14
-24 = b
Thus, the y-intercept of the other line is -24.
Therefore, the equation of the other line in slope-intercept form is y = -7/4x - 24
Step 3: Convert from slope-intercept form to standard form to find A, B, and C:
Now we can convert y = -7/4x - 24 to standard form by isolating -24 on the right-hand side:
First, let's multiply both sides by 4 to clear the fraction:
(y = -7/4x - 24) * 4
4y = -7x - 96
Now let's add -7x to both sides to convert from slope-intercept form to standard form:
(4y = -7x - 96) + 7x
7x + 4y = -96
Thus, 7 is A, 4 is B, and -96 is C.