Students are often asked to find the equation of a line that passes through a point and has a certain slope.. Watch the video tutorial below to understand how to do these prolems and, if you want, download this free worksheet if you want some extra practice.
Steps to follow:
Example: How to find the equation of a line that goes through the point (1, 3) and has a slope of 2.
What we know from the problem: that the slope is 2 so we can write y = 2x + b
Our goal: to find the y-intercept or "b"
Step 1) Substitute slope for 'm' in y = mx + b
y = mx +b
y = 2x + b
Step 2) Substitute the point (1,3) into equation
y = 2x + b
3 = 2(1) +b
Step 3) Solve for b
3 = 2+b
3-2 = 1= b
Step 4) Now that we know b, all that we have to do is put it into the equation and we now have our line in slope intercept form
y = 2x+1
Below is a picture of y = 2x + 1
Practice Problems
Try to write (or mentally make a note) of each equation below.
4) What is the equation of a line whose slope is 0 and that goes through the point (7,5)? Express the equation of this line in slope-intercept form.
Answer
There are two ways to approach this problem. First, you can look at this as a horizontal line, any horizontal line
has the standard form equation of y = b where b is the y intercept. Since the slope is 0, and only horizontal lines
have a slope of zero, all points on this line including the y-intercept must have the same y value. This y-value is 5, which we
can get from the fact that the line passes through the point (7,5). Therefore the standard form equation of this horizontal line
is y = 5.
Graphing Calc
28 = 30 + b