# Weekly Homework Sheet Q2 5

## Weekly Homework Sheet Q2 5

This article will explain the solution to the question 5 of the second quarter weekly homework sheet for the math class. The question is as follows:

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Write an equation of the line that passes through the point (3, -2) and is perpendicular to the line y = 2x + 5.

To solve this question, we need to find the slope and the y-intercept of the line that we are looking for. We can use the following steps:

Find the slope of the given line y = 2x + 5. The slope is the coefficient of x, which is 2.

Find the slope of the line that is perpendicular to the given line. The slope of a perpendicular line is the negative reciprocal of the original slope, which means we flip the fraction and change the sign. So, the slope of the perpendicular line is -1/2.

Use the point-slope form of a line to write an equation of the line that passes through the point (3, -2) and has a slope of -1/2. The point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Substituting the values, we get y - (-2) = -1/2(x - 3).

Simplify and rearrange the equation to get it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. To do this, we need to distribute -1/2 on the right side, add 2 to both sides, and then add 3/2 to both sides. We get y = -1/2x + 7/2.

Therefore, the equation of the line that passes through the point (3, -2) and is perpendicular to the line y = 2x + 5 is y = -1/2x + 7/2.