Equation for the line that is perpendicular to the line 4y=5x-8 through the point (-5,4)

To find the equation for this line, we are going to use point-slope form. First, to find the perpendicular slope, we need to find the slope of the line 4y=5x - 8. To do this, we must transform this equation into slope-intercept form so we can determine the slope.

4y=5x-8

We should divide both sides of the equation by 4 to put the equation into slope-intercept form.

4y/4 = 5x/4 - 8/4

y = 5/4x - 2

Therefore, we can determine that the slope of this equation is 5/4. The slope of the line perpendicular to this line has the opposite reciprocal slope. To find the opposite reciprocal of 5/4, we must make it negative and switch the numerator and the denominator. The opposite reciprocal of 5/4 is -4/5.

Now, we must use this slope and the point we were given, (-5, 4), to write a new equation.

y = m(x-h) + k

y = -4/5(x + 5) + 4

y = -4/5x - 4 + 4

y = -4/5x

Therefore, your answer is y = -4/5x.

Hope this helps!

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

the answer is ! ?