I need to know how to find the slope so I can graph the equations but I don't know how. For example, what is the slope of y= 2x + 1 ?
`y=2x + 1`
The given equation of the line is in slope-intercept form y=mx + b, where m is the slope and b is the y-intercept (0,b).
This indicates that in y=2x + 1, the slope is the number beside x.
Thus, slope is m=2.
Also, the y-intercept is the constant in the equation in y=2x+1.
Hence, the y-intercept is (0,1).
Using the y-intercept (0,1) and the slope m=2, the graph of y=2x+1 is:
The equation y=2x+1 is a linear equation. To find the slope, since it's already in the right format, you can use the standard equation y=mx+b, where m equals the slope. With the equation you have given, 2 would equal m and also be the slope of the equation. Some equations might not be this easy, but you can always put it into a graphing calculator.
Your equation is
Therefore since m is equal to the slope, the slope is 2.
If you need to find the slope using x and y coordinates do `m=(y2-y1)/(x2-x1)`
In your given equation, y = 2x + 1, the slope is 2. This is the slope intercept form, which has a general equation of y = mx + b where m is the slope and b is the y-intercept.
In other cases you could find the slope if you are given x and y points using the formula `m = ( y_2 - y_1 ) / (x_2 - x_1 )`
where x sub 1 is not equal to x sub 2.
whatever is in front of the x is the slope, so in this case, the slope is 2 because its 2x, and slope means rise/run so in this case, it would be 2/1 because you rise 2 and run 1 from the y-intercept which is (0,1), because y=mx+b where m is the slope, and b is the y-intercept.
y= 2x + 1
This is in the slope intercept form y = mx + b where m is the slope. So for this example, 2 is the slope.
Its also good to be familiar with the point-slope formula:
y - y1 = m(x - x1) where again, m is the slope.
When given standard form: Ax + By = C,
just rearrange into slope intercept form to figure out the slope.
The website I linked to runs through a quick and clear tutorial on the y-intercept form and how to find the slope as well as the y intercept.
For graphing purposes, in addition to knowing the slope you also need a starting point. Given the y-intercept form, its just easy to use the y-intercept. The y-intercept of a straight line is the point (0,y). The unknown y-intercept for the equation
y = 2x + 1
is simply positive 1.
Knowing that, graphing is easy.