How to write equation of a line, given the slope of a line and also one of points on the line.
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 problems and, if you want, download this free worksheet if you want some extra practice.
Video Tutorial on Equation from Slope and a Point
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"
Substitute slope for 'm' in y = mx + b
y = mx +b
y = 2x + b
Substitute the point (1,3) into equation
y = 2x + b
3 = 2(1) +b
Solve for b
3 = 2+b
3-2 = 1= b
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
Try to write (or mentally make a note) of each equation below.
Find "b", the y-intercept
y = ½x + b
Substitute in the point (2,3)
3 = ½(2)+ b
Solve equation for b
3 = 1 + b
3 - 1 = 2 = b
Insert b into equation
y = ½x +2
Below is graph of y = ½x +2
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.Step 1
y = 0x + b
Substitute x and y coordinates of point
5 = 0 • 7 + b 5 = b
Solve equation for B
b = 5
y = 0x + 5 y = 5