How do you find ther answer to a slope in algebra?

Question

Make up a question and solve it please
So i can see how you did it,
thank you

Answer 1

An architect is designing a house with a roof slope of 6" rise for every 12" of run (6/12). The neighborhood limits homes to no more than 16' high at roof peak. If the roof is 8'-6" at the wall face, how wide can he design the home, given the roof to be symmetrical.

Y=mX+b, where m=6/12 and b=8.5;

Y=1/2X+8.5
If Y=16, solve for X
16=1/2X+8.5
7.5=X/2
X=15, one half the house width (symmetry)

Alternate:

A symmetrical house 30' wide has a roof 8.5' at wall face, and 16' at the peak. What is the roof slope?

Y=mX+b; where X=15' (half of width - symmetry), Y=16', b=8.5'

16'=m*15'+8.5'
7.5'=m*15'
m=1/2 or 1/2' rise per 1' of run.

Answer 2

If an equation can be put in the form y = mx + b, then you have the equation of a line with slope 'm' and the line crosses the 'y' axis (has y intercept) (0,b).

Find the equation of the line that runs through the point (-1,3), and (2,7). The slope is the difference between the y's divided by the difference in x's. So,

7 - 3
------- = m
2 - (-1)

m = 4/3

So, now pick one of the points (let's use (2,7)) and find the equation for the point (x,y)

y - 7
------ = 4/3
x - 2

y - 7 = (4/3)(x - 2) or simplifying

y = (4/3)x - 13/3

HTH

Charles

Answer 3

Slope is "rise over run". It's a ratio of how much a line ascends as you go from left to right. If you're given two points on the line, the slope is going to be the change in y over the change in x. Or if the points are (x1, y1) and (x2, y2), then the slope is (y2-y1)/(x2-x1). For example if a line passes through points (4,11) and (2,7), then the slope is (11-7)/(4-2), or 4/2 = 2.

If you're given an equation for a line, and rewrite it in the form of y = mx + b, then m is always the slope. For exampe, if 2y + 5x = 1 is the equation of a line, you can solve for y and rewrite this as y = (-5/2)x + 1/2. So the slope of the line is -5/2.

Answer 4

What is the slope of the line 4x-8y=12?

First re write the equation to make y the subject

4x-12=8y

so y=4/8x-12/8 y=0.5x - 1.5

This is then of the form y=mx+c

where m is the slope of the line and c is its intercept to the x=0 axis

so the slope is 0.5

Answer 5

Slope formula

m = y₂- y₁/ x₂- x₁

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