Write the equation for the line containing the point -8,-4 and is perpendicular to 4x-3y=-17 write the equation in slope intercept form

Question

No decimals and no mix numbers

Answer 1

First, we must put the equation you gave into slop-intercept form, where it will be easy to see the slope. We do this through algebra:

4x-3y=-7

4x=-17+3y (add 3y to both sides)

4x +17 = 3y (add 17 to both sides)

4/3x + 17/3 = y (divide both sides by 3)

Now, we have the equation y=4/3x+17/3. Knowing that in this form y=mx+b, m is the slope. This means that the slope of this line is 4/3.

To find a perpendicular line, we know that it's slope will be the negative reciprocal. So, the slope of our new line is -3/4.

Now, we can plug this new slope, along with the given point (-8,-4) into our y=mx+b equation and solve for b, our y-intercept.

y=mx+b

-4=-3/4(-8)+b

-4=6+b (multiply -3/4 and -8)

-10=b (subtract 6 from both sides)

Here we found that the y-intercept of our perpendicular line is -10. Now we have all the pieces we need to write the equation of our new line in slope-intercept form:

y=-3/4x-10

We can check our work by plugging in the x-coordinate -8 and seeing if we get the correct y-coordinate of -4:

y=-3/4(-8)-10

y=6-10

y=-4

Therefore, the answer we found is correct.

Answer 2

4x -3y = -17

solve for y

3y = 4x+17

y = 4x/3+17/3

4/3 = the slope = the coefficient of the x term when the equation is solved for y

the perpendicular line has a negative inverse slope = -3/4

y= -3x/4 +b plug in the point to solve for b

-4 =-3(-8)/4 +b

b =-4 -6 =-10

the perpendicular line through the given point is

y=-3x/4 -10