Write the equation of the line that passes through the points (1, -6) and (8, 9). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.

Step-by-step explanation:

Point-slope form is represented by . To write an equation with it, we need the slope of the line and a point the line crosses through. We already have at least one point the line crosses through, so let's figure out the slope.

To find the slope, use the slope formula . and represent the x and y values of one point the line crosses, and and represent the x and y values of another point the line crosses. So, using the x and y values of (1, -6) and (8, 9), substitute them into the formula and solve:

Thus, the slope is .

2) Now, using the point-slope form of  ,  substitute , , and for real values in order to write an equation in point-slope form. The represents the slope, so substitute in its place. The and represent the x and y values of one point on the line. So, choose any one of the points given - either one is fine - and substitute its x and y values for and . (I chose (8,9)). This gives the following equation and