1. Plot the following points.
2. Form an equation.
3. Find the slope.
Some Helpful Tools
The Slope-Intercept Form
Now we have a coordinate pair of (1, 5).
This section will cover the fundamentals and rules of the slope-intercept form.
How to write an equation for a line when given the slope and the y-intercept.
Example: m = -3, b = 5
Begin by using the slope-intercept form.
y = mx + b
y = -3x + 5
The line for this equation will pass through the y-axis at (0,5), It is a negative slope, which means that we will go down 3 units and to the right 1 unit.
y = 2x + 3
y = 2(3) + 3
y = 6 + 3
y = 9
Because the line is going upward, the last number in the equation will be positive.
Notice how the line crosses the y-axis at positive 3, which means the last number in the equation will be positive 3.
To find the slope, let's choose two of the three points to help locate the other points on the line.
Let's choose points (1,5) and (2,7) as set one and set two.
To find the slope, we'll subtract the second set from the first set beginning with the value for y as shown below.
(3,9)
(2,7)
(1,5)
y = 2x + 3
y = 2(2) + 3
y = 4 + 3
y = 7
y = 2x + 3
y = 2(1) + 3 y = 2 + 3
y = 5
Finding the Solutions
Plotting Points
Using the points that we have found, we'll plot our points in our coordinate plane.
Example 1:
Example 2: y = -3x + 2
The slope is -3
The y-intercept is 2.
This means that the line intersects the y-axis at (0,2). We can choose the following numbers for x. Let's choose 1, 2, and 3.
The slope is -3. This means we can move down 3 units and across 1 unit to find any point on the line.
Example 3:
Begin by finding three numbers to represent x. Let's try 2, 4, and 6.
This section will combine the Intercepts Tutorial and the Slope of a Line Tutorial.
The slope-intercept form is:
y = mx + b
The slope of the line is m, and the y-intercept is b. This form is used to graph the solutions of an equation in a coordinate plane.
Example: y = 2x + 3
To find the solution to this equation, let's randomly choose the number 3 for x. Plug 3 into the value for x.
Since we already know the value for x is 3, we now have a coordinate point of
(3, 9).
In order for the graph to have many points, let's choose another number for x. This time, we'll choose the number 2.
This will give us another coordinate point of (2, 7).
Lastly, let's choose 1.
Math: Slope-Intercept Form - Tutorial
