Determine the equation of each of the following lines?

Question

The slope is -2 and the point (2, -3) is on the line. 
The line passes through the points (-3, 3) and (6, 9).

 

?

Answer 1

We can express the equation of a line in slope-intercept, or y = mx + b form, where m = the slope and b = the y-intercept.

 

For the first line, we are given a point (x, y) on the line, which is (2, -3). We are also told that the slope m = -2. Let's plug these values into the y = mx + b form of the equation of a line to find b.

 

-3 = -2(2) +  b

-3 = -4 + b

1 = b

 

The equation of this line can be written as y = -2x + 1

 

For the second line, we can determine the slope by finding the difference of the two y-coordinates given divided by the difference of the two x-coordinates given.

 

m = (9 - 3)/(6 - (-3)) = 6/9 = 2/3

 

Now that we have the slope, can you now use the technique we used in the first problem to find the equation of the line for the second problem, Greg?