How to Find the Equation of a Line Given Two Points

When working with linear equations, one common task is to find the equation of a line that passes through two given points. This process involves using the slope-intercept form of a line equation, which is y ax b, where a is the slope of the line, and b is the y-intercept.

Step-by-Step Guide

Let's consider two points: (-1, -4) and (-5, -2). The goal is to find the equation of the line that passes through these points.

Step 1: Determine the Slope (a)

The slope of the line can be calculated using the slope formula:

m frac{y_2 - y_1}{x_2 - x_1}

Plugging in our points (-1, -4) and (-5, -2), we get:

m frac{-2 - (-4)}{-5 - (-1)} frac{2}{-4} -frac{1}{2}

Step 2: Use a Point and the Slope to Find the y-Intercept (b)

Now, we need to find the y-intercept, b. We can use one of the given points and the slope in the equation y ax b. Let's use the point (-1, -4):

-4 -frac{1}{2}(-1) b

Solving for b:

-4 frac{1}{2} b

b -4 - frac{1}{2} -frac{8}{2} - frac{1}{2} -frac{9}{2}

Step 3: Write the Equation of the Line

Now that we have both the slope and the y-intercept, we can write the equation of the line:

y -frac{1}{2}x - frac{9}{2}

We can also write it in the form:

2y -x - 9

Multiplying through by 2 gives:

x 2y -9

Additional Resources

If you need further practice or have similar questions about finding the equation of a line given two points, you can explore related questions on platforms like Quora. Here are a few example questions to explore:

Find the equation of the line that passes through the points How do you find an equation for the line that passes through the points? Equation of a line through two points

Remember, understanding the process and practicing with different sets of points will help you master this skill.