Math Question Equation

Question

Point-Slope equation for the line that has slope 3 and passes through the point (5, 21)

Answer 1

The equation of a line written in point-slope form will follow the "model" : y = mx + b where m is the slope and b is the y-intercept.

For this problem, the slope, m, is given to you as 3. Therefore we can start by writing:

y = mx + b

y = 3x + b

To find b , we can use the coordinates of the point given to you and substitute a and y into the equation we started and solve for b:

y = 3x + b

21 = 3 *5 + b

21 = 15 + b

21-15 = 15 + b -15

6 =b

As a result, the equation of the line written in point-slope form will be:

y = 3x + 6

Answer 2

The point slope equation (y - y_o) = m(x - x_o) where m = slope and (x_o,y_o) is a point on the line

So,

(y - 21) = 3(x - 5) = 3x - 15 or y = 3x + 6