154k views
2 votes
7. Write the slope-intercept form of the equation that passes through the point (2, 3) and is perpendicular to the line y = 5/8x - 4 y = 5/8x + 17/4 y = -5/8x + 7/4 y = -8/5x + 31/5 y = -8/5x - 31/5

User Mishac
by
7.4k points

1 Answer

5 votes

Answer:

y = -8/5 x + 31/5

Explanation:

Write the slope-intercept form of the equation that passes through the point (2, 3) and is perpendicular to the line y = 5/8x - 4 y = 5/8x + 17/4 y = -5/8x + 7/4 y = -8/5x + 31/5 y = -8/5x - 31/5

The slopes of perpendicular lines are negative reciprocals.

Slope of given line: 5/8

Slope of perpendicular line: -8/5

Point on perpendicular line: (2, 3)

Slope-intercept form of the equation of a line:

y = mx + b

We know the slope of the perpendicular is -8/5, so now we have

y = -8/5 x + b

We need to find b.

We use the given point for x and y and solve for b.

y = -8/5 x + b

3 = -8/5 * 2 + b

15 = -8 * 2 + 5b

15 = -16 + 5b

5b = 31

b = 31/5

Now that we know that b = 5, we can write the equation of the perpendicular line:

y = -8/5 x + 31/5

User Parmanand
by
7.5k points

No related questions found

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

9.4m questions

12.2m answers

Categories