Write the equation of the line that satisfies the given condition: contains the point (10, -3) and is perpendicular to the line 4 x + 3 y = -8.
A) 3 x + 4 y = 42
B) 3 x - 4 y = 42
C) 3 x - 4 y = 18
D) 3 x + 4 y = 18

Question

Quizplus · Accepted Answer

To find the equation of a line perpendicular to another line, we need to use the fact that the slope of the perpendicular line is the negative reciprocal of the slope of the original line.

The original line has the equation 4 x + 3 y = -8. We can rewrite this equation in slope-intercept form by solving for y:

3 y = -4 x - 8
y = (-4/3) x - (8/3)

So the original line has a slope of -4/3. The perpendicular line will have a slope that is the negative reciprocal of this, which is 3/4.

Now we can use the point-slope form of the equation of a line to write the equation of the perpendicular line. We know it passes through the point (10, -3), so we have:

y - (-3) = (3/4) (x - 10)

Simplifying this equation, we get:

y + 3 = (3/4) x - (30/4)

y = (3/4) x - (33/4)

This is the equation of the line that is perpendicular to the original line and passes through the point (10, -3). We can rewrite this equation in the standard form Ax + By = C:

3 x - 4 y = 42

Therefore, the answer is B.

Write the Equation of the Line That Satisfies the Given