Question

Given points (x₁, y₁) and (x₂, y₂), find the equation and slope of the line.

a) y = mx + b, m = (y₂ - y₁)/(x₂ - x₁), b = y₁ - mx₁
b) y = mx + b, m = (x₂ - x₁)/(y₂ - y₁), b = y₁ - mx₁
c) y = mx + b, m = (y₂ - y₁)/(x₁ - x₂), b = y₁ - mx₁
d) y = mx + b, m = (x₁ - x₂)/(y₂ - y₁), b = y₁ - mx₁

Answer 1

The correct option for the equation and slope of a line using two points is a) y = mx + b, with m = (y₂ - y₁)/(x₂ - x₁) representing the slope, and b = y₁ - mx₁ for the y-intercept.

Step-by-step explanation:

To find the equation and the slope of the line given two points (x₁, y₁) and (x₂, y₂), you use the slope-intercept formula y = mx + b, where m is the slope and b is the y-intercept. The correct formula to calculate the slope m is m = (y₂ - y₁)/(x₂ - x₁). This represents the rise over run or the change in y over the change in x between the two points.

Once you have the slope, you can find the y-intercept b using the equation b = y₁ - mx₁. With both m and b calculated, you can write the equation of the line.

The correct choice from the given options would therefore be: a) y = mx + b, m = (y₂ - y₁)/(x₂ - x₁), b = y₁ - mx₁.