Find the equation (in terms of
) of the line through the points (-3,-4) and (1,8)

To find the equation of the line passing through the points \((-3, -4)\) and \((1, 8)\), we can use the point-slope form of the equation of a line. The point-slope form is given by:

\[ y - y_1 = m(x - x_1) \]

where \((x_1, y_1)\) is a point on the line and \(m\) is the slope of the line.

First, let's calculate the slope \(m\) using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting the given points \((-3, -4)\) and \((1, 8)\):

\[ m = \frac{8 - (-4)}{1 - (-3)} = \frac{8 + 4}{1 + 3} = \frac{12}{4} = 3 \]

So, the slope \(m\) is 3.

Next, we'll use the point-slope form with one of the points. Let's use the point \((1, 8)\):

\[ y - 8 = 3(x - 1) \]

Now, we'll simplify this equation to get the slope-intercept form \(y = mx + b\):

\[ y - 8 = 3x - 3 \]
\[ y = 3x - 3 + 8 \]
\[ y = 3x + 5 \]

Therefore, the equation of the line passing through the points \((-3, -4)\) and \((1, 8)\) is:

\[ y = 3x + 5 \]

Would you like more details or have any questions?

Here are 5 related questions you might want to ask:
1. How do you find the equation of a line given its slope and a point on the line?
2. What is the general form of the equation of a line?
3. How do you convert from point-slope form to slope-intercept form?
4. How can you determine if two lines are parallel?
5. What is the formula for finding the distance between a point and a line?

Tip: When finding the equation of a line, ensure to calculate the slope accurately and choose the correct form of the equation (point-slope, slope-intercept, or general form) for your needs.

Learn how to find the equation of a line passing through the points (-3, -4) and (1, 8) using the point-slope form. This problem covers key concepts in coordinate geometry and linear equations, including calculating slopes and transforming equations between forms. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation