What are three ways to find the slope of a line?
Answers
The slope of a line is a measure of how fast it is changing. This can be for a straight line -- where the slope tells you exactly how far up (positive slope) or down (negative slope) a line goes while it goes how far across. Slope can also be used for a line tangent to a curve. Or, it can be for a curved line when doing Calculus, where slope is also known as the "derivative" of a function. Either way, think of slope simply as the "rate of change" of a graph: if you make the variable "x" bigger, at what rate does "y" change? That is a way to see slope as a cause and an effect event.
Y=mx + b
1
Use slope to determine how steep, and in what direction (upward or downward), a line goes. Finding the slope of a line is easy, as long as you have or can setup a linear equation. This method works if and only if:
There are no exponents on the variables
There are only two variables, neither of which are fractions (for example, you would not have {\displaystyle {\frac {1}{x}}}
The equation can be simplified to the form {\displaystyle y=mx+b}, where m and b are constants (numbers like 3, 10, -12, {\displaystyle {\frac {4}{3}},{\frac {3}{5}}}).
2
Find the number in front of the x, usually written as "m," to determine slope. If your equation is already in the right form, {\displaystyle y=mx+b}, then simply pick the number in the "m" position (but if there is no number written in front of x then the slope is 1). That is your slope! Note that this number, m, is always multiplied by the variable, in this case an "x." Check the following examples:
• 2y-3=8x+7
• 2y-3(+3)=8x+7(+3)
• 2y=8x+10
• 2y÷2=8x+10÷2
• y=4x+5
Answer. => m=4