What is an equation of the line that is perpendicular to y=−4/5x+3 and passes through the point (4, 12) ?

1 answer:

3 0

The slope of the given line is -4/5. The line perpendicular to that line will have a slope that is the opposite reciprocal. In other words, the perpendicular slope will be 5/4. If it passes through (4, 12), we have an x and a y value to use in y=mx+b. y is 12, x is 4, and we have a slope of 5/4. Filling in accordingly: $12= \frac{5}{4}(4)+b$ and 12 = 5 + b. So b = 7. Rewriting with our new slope and b value, $y= \frac{5}{4}x+7$ . And there you go!

You might be interested in

If the function f(x) = -1/2x - 7 were graphed, which of the following would be true?

Fittoniya [83]

ANSWER

D. As the x-values increase, the y-values would decrease

EXPLANATION

The given function is
$y = - \frac{1}{2} x - 7$

The slope of this function is
$m = - \frac{1}{2}$

Since the slope is negative, there is a negative or an inverse relationship between x and y.

As the values of x increases, the values of y decreases.

Also, as the values of x decreases, the values of y increases.

The first option is not true because as x is becoming bigger and bigger negatively, y will become positive.

For instance, when
$x = - 40$
$y = - \frac{1}{2} ( - 40) - 7$

This implies that,

$y = 20 - 7 = 13$

Options B is obviously not true because the function has a negative relationship between x and y.

Option C is also false because, x can be positive since it is the independent variable.

See graph

Therefore, the correct answer is option D.