Unit 4.3 Slope Intercept Form and Point Slope Form
Slope Intercept Form
Slope intercept form a way to write the equation of a line.
Slope Intercept Form
y = m(x) + b
- y is the “y coordinate”
- m is the slope of the line (how steep the line increases or decreases)
- x is the “x coordinate”
- b is the y-intercept
The slope of the line is how “steep” the line is. If you have a positive slope, your line increases, and if your slope is negative, your line decreases. You can find the slope (m) of a line using 2 ordered pairs and the slope equation.
Slope Equation
Slope will always be “rise”, or the y values, over “run”, the x values.
Lines that are parallel, or will never intersect will have the same slope. Lines that are perpendicular, or intersect at a 90° angle, will have inverse slopes
Finding the slope intercept equation from two ordered pairs
Find the slope intercept equation for the line that goes through (1,2) and (3,4)
First thing is to write out your ordered pairs
(1,2) is your first ordered pair and (3,4) is your second ordered pair
Define your values as x1 , y1 and x2, y2 and write out the values
Next, find the slope of the line using the slope formula
The slope of this line is 1
We now have the slope (m), and an x value and y value. To find the intercept, pick either of the two ordered pairs (it doesn’t matter which one) and plug it into your slope intercept equation
For this example, ordered pair 2, (3,4) was selected and plugged in for x and y.
b = 1, therefore the equation of the line is
y = 1(x) + 1 or y = x + 1
Point Slope Form
Point slope form is another way to write an equation for a line
Point Slope Form
y − y1 = m(x − x1)
- y and x are unknown y and x values
- y1 and x1 are known ordered pair points
- m is the slope of the line
Find the point slope equation from two ordered pairs
Find the point slope form of the line through points (3,4) and (5,6)
First thing is to write out the ordered pairs and which values are x1 , y1 , x2 and y2
Using the slope formula, find the slope of the line
Plug in your slope into the point slope form, and your values for x1 and x2
Standard Form
Ax + By = C
Where:
- x and y are ordered pair coordinates
- A, B and C are all real numbers