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a line has the equation 7x + 4y = -83 what is the equation of parallel line going through the point (-8,-10) the equation is given by Ax + By = C. Find A, B, and C.​

User Warface
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1 Answer

3 votes

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.

User JDutil
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