Write a linear equation when given a point (x, y) and a slope m

Write the equation of the line that passes through the point (-2,-3) and has a slope of 5.


We know that m = 5 because the slope is given, so y = 5x + b is a partial answer.

With the information (-2, -3) a common mistake is to try graphing two points at (-2,0) and (0, -3).
(-2, -3) represents only one point, and we don't have a graph that shows other points.

We use x = -2 and y = -3 to fill in the slope-intercept form equation to get -3 = 5 (-2) + b.
Now we have three out of four pieces, and we solve for the unknown b.    -3 = -10 + b,
then add 10 to both sides.


b = 7


In college math we often use an intermediate answer to go back to the beginning of the problem to find the final answer.  Here we use b = 7 in the y = mx + b that we started with.

y = mx + 7     and that becomes y = 5x + 7 when we pu in the slope.

The answer has the variables x and y in the equation, not the values -2 and -3, because the equation of a line represents the values of all possible points on the line.