Question

What is the y-intercept of the line perpendicular to the line...

Answer 1

Answer:

D) 5

Step-by-step explanation:

Perpendicular lines have opposite reciprocal slopes.

The line: $y=\frac{3}{4} x+3$ has a slope of $\frac{3}{4}$ as it is  in y=mx+b form, where m is the slope, and b is the y-intercept.

Since the slope is $\frac{3}{4}$, we see that the negative reciprocal slope is $-\frac{4}{3}$, as $\frac{4}{3}$ is the reciprocal (flip the numerator and denominator).

From here, we can use point slope form: $y - y1 = m(x- x1)$, where $(y1, x1)$ is  the point. In this case, (3, 1) is the point.

Thus, we have: $y-1 =-\frac{4}{3}(x-3)$ as our final equation.

Simplifying: $y-1 = -\frac{4}{3}x+4$

And: $y=-\frac{4}{3}x+5$, which gives us the y-intercept to be 5.

Let me know if this helps!