Finding the Equation of Any Line Which is Not Vertical
Most applications of lines involve lines which are neither vertical nor horizontal. Every line which is not vertical can be written in the form
where m is the slope of the line, and the number b is the y-intercept of the line. This form of the equation of a line is called the slope-intercept equation of a line. The y-intercept is the point where the line crosses the y-axis. The x-coordinate of the y-intercept of a graph is always zero.
Example 12. Find the equation of the line having slope 5 and passing through the point (0,2).
Answer:
y = 5x + b
2 = 5(0) + b replacing y with 2 and x with 0 to find b.
2 = b
Example 13. Find the equation of the line having slope 7 and passing through the point (2,9).
Answer:
y = 7x + b
9 = 7(2) + b replacing x with 2 and y with 9.
9 = 14 + b
-5 = b
Example 14. Find the equation of the line with slope -4 and passing through the point (-1,2).
Answer:
y = -4x + b
2 = -4(-1) + b
2 = 4 + b
-2 = b
