Write a linear equation in slope intercept from that is perpendicular to x−3y=3 and passes through the point (5, −9).

Step-by-step explanation:

First, let’s determine the slope of the original equation.

We have

Subtract x from both sides and then divide both sides by -3. So:

Therefore, the slope of our original line is 1/3.

Remember that perpendicular lines have slopes that are negative reciprocals of each other.

Therefore, the slope of our new perpendicular line is the negative reciprocal of 1/3.

Thus, the slope of our new line will be -3. We flip the fraction and add a negative.

So, the slope of our new line is -3. We also know that it passes through the point (5, -9).

Now, we can use the point-slope form:

Where m is the slope and (x₁, y₁) is a point.

So, substitute -3 for m and (5, -9) for (x₁, y₁). This yields:

We want our line in slope-intercept form. So, distribute the right:

Subtract 9 from both sides. Therefore, our equation is:

the range is 19

step-by-step explanation:

the range is biggest number minus the smallest, so in this case it would be

41 - 22 = 19

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