Question

A line with slope -1/2 passes through point Q (6, 7). Does point S (2, 5) lie on this line?

Answer 1

Answer: No

Find the equation of the line using slope-intercept form: y = mx + b
y = -1/2x + b                                                                                  ^      ^ 
                                                                                                 slope   y-intercept

Find b, the y-intercept (where the line intersects the y-axis) by substituting the coordinates of point Q (6, 7).
y = -1/2x + b                 Subtitution
7 = -1/2(6) + b               Simplify
7 = -3 + b                     Add 3 to both sides
10 = b                           Isolated b
b = 10                           Isolated b

Using the above information, find the equation of the line.
y = -1/2x + b
y = -1/2x + 10

To find if point S (2,5) lies on the line, substitute in its coordinates in the equation of the line. 
y = -1/2x + 10             Substitution
5 = -1/2(2) + 10          Simplify
5 = -1 + 10                  Simplify
5 = 9            -->         If the statement is true, the point lies on the line. 
                                  If the statement is false, the point does not lie on the line.

In this case, 5 does not equal 9. Therefore, point S does not lie on the line.