A line with a slope of 4 passes through the point (2,1). What is the equation of the line?

Question

how do you solve it

Answer 1

You can either use the point-slope form or slope-intercept form to determine the equation of the line.

Using point-slope:

y - y₁ = m(x - x₁) where (x₁,y₁) is the point the line passes through with m as the slope.

y - 1 = 4 (x - 2)

y - 1 = 4x - 8

y = 4x - 7

Using slope-intercept:

y = mx + b, where m is the slope and b is the y-coordinate of the y-intercept. In this case you do not know b. But the fact that the point passes through (2, 1) means when x = 2, y = 1.

1 = 4(2) + b

1 = 8 + b

b = -7.

Now that you know the value for b:

y = 4x - 7