Math Help Slope-Y-Intercept?

Question

Write in slope-y-intercept form an equation of a line perpendicular to 4x-5y+20=0 that passes through the point (5,3). Any help would be greatly appreciated and best answers will be given out.

Answer 1

You have to find the slope of your line first.
5y = 4x+20;
y = 4/5x + 4

so the slope is 4/5.

The slope of a line perpendicular to this line will have a negative reciprocal slope, or -5/4

Using the point slope form and the point provided (5.3), we get:

(y-3) = -5/4(x-5)
4y - 12 = -5x + 25
4y = -5x + 37
y = -5/4x + 37/4

Check my work :)

Answer 2

One way to do this problem is to find the slope of the line given by putting that equation in slope-intercept form.
4x-5y+20 = 0
4x + 20 = 5y
y = (4/5)x + 4
Now you know that the slope of the original line is (4/5).
The slope of the perpendicular line is the negative reciprocal of the slope of the original line, thus the slope of the desired line is (-5/4).
With the given point and the slope we just found, we can now write the equation of the desired line in point-slope form:
y-3 = (-5/4)(x-5)
distribute the right side out:
y-3 = (-5/4)x + 25/4
add 3:
y = (-5/4)x + (25+12)/4 = (-5/4)x + 37/4
which is the desired line in slope-intercept form.

Answer 3

Before you just take it as a fact that a perpendicular has a slope that is the negative reciprocal of the original line, draw some other lines to convince yourself this is true.

Draw a line with slope 1, then a line with slope -1/1.

Draw a line with slope 2, then a line with slope -(1/2).

Once that is clear, use y=mx+b. Plug in your m and the (x,y)=(5,3) from the point where your equation must hold (so that the point is on your line). Solve for b.

Answer 4

it is important to apply y=mx+b, m being the slope and b being the y-intercept. locate the slope by potential of employing y2-y1 / x2 - x1. on your equation, it comes out as -2 - 0 / 0 - 4 which equals -2/-4 which equals a million/2. it is the slope now plug interior the slope with between the factors to locate the y intercept. 0 = a million/2(4) + b equals 0 = 2+b which equals b=-2. So your equation is y = 0.5x - 2. you are able to deduct that the slope is a million/2 and your y-intercept is -2.

Answer 5

4x - 5y + 20 = 0
5y = 4x + 20
y = (4/5).x + 4
Gradient of perpendicular = - 5 / 4
Passes thro` (5,3)
y - 3 = (- 5 / 4).(x - 5)
y = (- 5/4).x + 25/4 + 12/4
y = (- 5/4).x + 37/4