Final answer:
The equation of a line in point slope form containing the points (–2, 3) and (–1, –2) is calculated by first determining the slope (m = –5) and then using one of the points to write the equation as y – 3 = –5(x + 2), where point slope form is (y - y1) = m(x - x1).
Step-by-step explanation:
To write the equation of a line in point slope form, you need a point on the line and the slope of the line. The point slope form of a line's equation is typically written as (y - y1) = m(x - x1), where m stands for the slope and (x1, y1) represents a point through which the line passes.
Given two points (–2, 3) and (–1, –2), the first step is to calculate the slope using the formula m = (Y2 - Y1) / (X2 - X1). By substituting into this formula, we get m = (–2 – 3) / (–1 – (–2)) which simplifies to m = (–2 – 3) / (1) = –5. Now that we have the slope, we can use one of the given points and the slope to write the equation in point slope form as y – 3 = –5(x + 2).
It's important to understand that the terms b and m from a standard linear equation (y = mx + b) represent the y-intercept and the slope, respectively. In general, for a straight line graphed on a coordinate plane, the slope is constant and is calculated by the rise (change in y) over the run (change in x). For example, if a line has a slope of 3, it means that for every one unit increase in x, y increases by three units.