Question

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

Answer 1

Answer:

y = -8/5 x + 31/5

Step-by-step 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