The slope of the line is , so as x moves over 5 y moves up 4:
Then we connect the dots:
Find the equation of the line graphed below.
The y-intercept is -3. Since y decreases by 4 when x increases by 7, the slope of the line is . Therefore, the equation of the line is
Find, in slope-intercept form, the equation for the line that goes through the points (-3, 2) and (2, -4).
While the problem didn't give us a picture, we know part of the line will look like this:
From the graph, we find the rise and run between the two points:
Now we can find the slope, m, of the line:
We know that the equation of the line will look like
We can use one point on the line to find b, and the other point to check our answer.
To find b, let's use the point (-3, 2). We plug the values x = -3, y = 2 into the linear equation and solve for b:
Now we think the linear equation we want is
However, we've been wrong before. It was just one time, and we weren't going on much sleep, but still...it's possible. To eliminate the slim chance that we messed something up, let's check our answer with the point (2, -4).
The left-hand side of the equation will be -4
and the right-hand side of the equation will be ,
which, happily, also equals -4. The point (2, -4) is also on the line, like it's supposed to be, so we found the right equation.