50.7k views
3 votes
Write the equation of the line which is perpendicular to the line through the points (9, 10) and (3, -2) and passes through the x-intercept of the line.

a) y = -x - 7
b) y = 2x + 7
c) y = -x + 7
d) y = 2x - 7

1 Answer

6 votes

Final answer:

The equation of the line perpendicular to the one through (9, 10) and (3, -2) that passes through the line's x-intercept is not present in the given options, as the correct equation should be y = -1/2x + 7, based on the provided steps of finding the negative reciprocal of the original line's slope and determining the y-intercept of the perpendicular line.

The correct option is not given.

Step-by-step explanation:

The goal is to find the equation of a line that is perpendicular to the line passing through the points (9, 10) and (3, -2) and that goes through the x-intercept of this line. To start, we calculate the slope of the given line, which is ∆y / ∆x = (10 - (-2)) / (9 - 3) = 12 / 6 = 2.

The slope of the perpendicular line will be the negative reciprocal, which is -1 / 2. We know the original line crosses the x-axis when y equals zero. So, for the line y = 2x + b, finding the x-intercept gives us 0 = 2x + b. Solving for x when y = 0 gives us x = -b/2.

As the x-intercept is a point on both lines, we can use it to find the equation of the perpendicular line. If x = -b/2, then using the slope -1/2, the y-intercept 'c' of the perpendicular line can be found by substituting into y = (-1/2)x + c.

The correct equation that satisfies these conditions is y = -1/2x + 7, none of the given options match this exact form, so the answer would be 'none of the above' if this were a forced choice. However, the original question does not provide the correct options given the calculations.

The correct option is not given.

User Lavanda
by
9.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.