Find the equation of a line with the properties given. Write the equation in the form indicated.
-Passing through (3, 3) and perpendicular to the line whose equation is -9x + y = 5; slope-intercept form
D) y = - 9x - 30

Question

Quizplus · Accepted Answer

We first need to find the slope of the line -9x + y = 5. We can rearrange the equation to slope-intercept form (y = mx + b) by adding 9x to both sides:
y = 9x + 5
So the slope of this line is 9.

Since we want a line perpendicular to this one, we know that the slope of our new line will be the negative reciprocal of 9, which is -1/9.

Now we can use the point-slope form of a line to find the equation of our new line:
y - 3 = (-1/9)(x - 3)

To convert to slope-intercept form, we can distribute the -1/9 and then add 3 to both sides:
y - 3 = (-1/9)x + 1
y = (-1/9)x + 4

So the equation of the line passing through (3,3) and perpendicular to -9x + y = 5 in slope-intercept form is y = (-1/9)x + 4. Therefore, the best choice is C.

Find the Equation of a Line with the Properties Given