Point Slope
Point slope form is a way to represent a linear equation with two variables, usually denoted as (x, y), in the form y – y1 = m(x – x1)
Point slope form is a way to represent a linear equation with two variables, usually denoted as (x, y), in the form y – y1 = m(x – x1). The point (x1, y1) represents a specific point on the line, and m represents the slope of the line.
To better understand point slope form, let’s work through an example.
Example: Find the equation of a line that passes through the point (2, 3) with a slope of -2.
Step 1: Identify the given point and slope.
Given point: (2, 3)
Given slope: -2
Step 2: Substitute the values into the point slope form equation.
Using the point slope form equation, we have:
y – y1 = m(x – x1)
Substituting the values we identified:
y – 3 = -2(x – 2)
Step 3: Simplify the equation.
Distribute the -2 on the right side of the equation:
y – 3 = -2x + 4
Step 4: Rearrange the equation.
To isolate y, we can get the equation in the form y = mx + b (slope-intercept form).
Adding 3 to both sides of the equation, we get:
y = -2x + 7
Step 5: Interpret the equation.
The equation y = -2x + 7 represents a line with a slope of -2 passing through the point (2, 3). This equation describes the relationship between x and y values, where for each x value, the corresponding y value is determined by multiplying the x value by -2 and adding 7 to it.
In summary, point slope form is a useful tool for representing linear equations when a specific point on the line and the slope of the line are known.
More Answers:
Proving Congruence of Isosceles Triangles: Using the Side-Side-Side (SSS) CriterionExploring the Angle Bisector Theorem: The Incenter, Proportions, and Equidistance
Understanding the Circumcenter in a Triangle: Properties and Applications