What is the equation of a line thats passes through point (10, 5) and is perpendicular to the line whose equation is y=5/4x-2

y = -4x/5 + 13

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

c represents the y intercept

m represents the slope of the line.

The equation of the given line is

y = 5x/4 - 2

Comparing with the slope intercept form, slope = 5/4

If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line.

Therefore, the slope of the line passing through (10, 5) is - 4/5

To determine the y intercept, we would substitute m = - 4/5, x = 10 and y = 5 into y = mx + c. It becomes

5 = - 4/5 × 10 + c

5 = - 8 + c

c = 5 + 8 = 13

The equation becomes

y = -4x/5 + 13