Lines and Slope: Writing Linear Equations

The equation of a line in slope-intercept form:

-  To write the equation of a line, first identify the slope.
-  Find the y-intercept. This can be done by substituting the slope and the coordinates of a point on the line.

Examples:
Example 1.  What is the equation of the line that passes through and has a slope of ?
Solution: The general slope-intercept form of the equation of a line is
, where is the slope and is the -intercept.
By substitution of the given point and given slope:

. So, , and the required equation of the line is:

Example 2.  Write the equation of the line through two points and .
Solution: First, find the slope:
To find the value of , use either points and plug in the values of and in the equation. The answer will be the same: . Let’s check both points. Then:
.
The -intercept of the line is 4. The equation of the line is:

Example 3.  What is the equation of the line that passes through  and has a slope of ?
Solution: The general slope-intercept form of the equation of a line is
, where is the slope and is the -intercept. By substitution of the given point and given slope:
So, , and the equation of the line is: