Question

How do you write a linear equation given the slope and a point that is not the y-intercept?

A) y = mx + b
B) y - y₁ = m(x - x₁)
C) y = mx
D) y = b + mx

Answer 1

To write a linear equation with a given slope and point, use the point-slope formula y - y1 = m(x - x1), substitute the slope and point values, and then rearrange to the slope-intercept form y = mx + b.

Step-by-step explanation:

To write a linear equation given the slope and a point (x₁, y₁) that is not the y-intercept, you can use the point-slope form of the linear equation, which is: y - y₁ = m(x - x₁). In this formula, m represents the slope, and (x₁, y₁) are the coordinates of the given point. You will substitute these values into the equation. For example, if the slope (m) is 2 and the given point is (3, 4), then the equation would be written as y - 4 = 2(x - 3). To find the slope-intercept form y = mx + b, expand and simplify to y = 2x - 6 + 4, which simplifies further to y = 2x - 2.