|
Question 135820: Is there an easy way to find the slope of a line whose function is stated as an inequality of y=m+b? For example: 5(x+y)=20+3x How would this be put into y=mx+b form?
Found 2 solutions by scott8148, solver91311:
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! you are just solving for y in terms of x
dividing by 5 __ x+y=4+(3/5)x __ subtracting x and rearranging __ y=(-2/5)x+4
m=-2/5 and b=4
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website! First of all, let's get your terminology straight. y = m + b is not an inequality, it is an equation. And I rather suspect you meant y = mx + b.
What I think you meant to ask was:
Is there an easy way to find the slope of a line when the equation is in a form other than the slope-intercept form, y = mx + b?
There are two ways to find the slope, if that is the only piece of information that you need. I'll let you decide which is 'easy.'
Method 1:
First, remove any parentheses by using the distributive property, and then collect all like terms. There has to be one and only one term with an x in it, and one and only one term with a y. (exceptions: equations of horiziontal lines, 0 slope, have no x term, and equations of vertical lines, undefined slope, have no y term). Once you have the terms collected, divide the coefficient on x by the coefficient on y. If the x and y terms are on opposite sides of the equal sign, you have your answer. If they are both on the same side of the equal sign, you need the opposite or additive inverse of the coefficient fraction.
Method 2:
Solve the equation for y. That is manipulate the equation so that y with a coefficient of 1 is the only thing on the left side of the equation and everything else is on the right in simplest form with a single x term and a single constant term. Use the standard techniques of using the distributive property, collecting like terms, adding things to both sides, and multiplying both sides by the same quantities to achieve the desired result.
Distributive property:
Add -5x to both sides and collect terms:
Multiply both sides by 
The slope is then the coefficient on x and the constant value is the y-intercept, or the point on the y-axis intersected by the graph of the equation.
So, which is easier? You decide. I prefer Method 2, but that is just me.
|
|
|
| |
