What is the point slope form of the line passing through: (5,7),(6,8)?

1 Answer
Mar 4, 2018

See a solution process below:

Explanation:

First, we need to determine the slope of the line passing through the two points. The slope can be found by using the formula: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))#

Where #m# is the slope and (#color(blue)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the two points on the line.

Substituting the values from the points in the problem gives:

#m = (color(red)(8) - color(blue)(7))/(color(red)(6) - color(blue)(5)) = 1/1 = 1#

Now, we can use the point-slope formula to write the equation of the line. The point-slope form of a linear equation is: #(y - color(blue)(y_1)) = color(red)(m)(x - color(blue)(x_1))#

Where #(color(blue)(x_1), color(blue)(y_1))# is a point on the line and #color(red)(m)# is the slope.

Substituting the slope we calculated and the values from the first point in the problem gives:

#(y - color(blue)(7)) = color(red)(1)(x - color(blue)(5))#

#y - color(blue)(7) = x - color(blue)(5)#

We can also substitute the slope we calculated and the values from the second point in the problem giving:

#(y - color(blue)(8)) = color(red)(1)(x - color(blue)(6))#

#y - color(blue)(8) = x - color(blue)(6)#