Equation of the line through point (5,4) and perpendicular to y=−4/3x−2.

y=3/4x+1/4

Step-by-step explanation:

Perpendicular lines have slopes that are negative and reciprocal. If you multiply them together, the result is -1.

So, to find the slope of the new line, we can use this equation:

-4/3m=-1

multiply both sides by 3/-4

m=3/4

So the slope of the new line is 3/4

Here's the equation so far:

y=3/4x+b (b is a placeholder)

we can substitute the point (5,4) into the equation, since the line is going to pass through it.

4=3/4(5)+b

4=15/4+b

1/4=b

So the line is y=3/4x+1/4

Hope this helps!

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step-by-step explanation: