Find an equation for the line with the given properties. Express your answer using either the general form or the​ slope-intercept form of the equation of a line.
Slope=3​; containing the point ​(-2​,-1​)


To find the equation of a line with a given slope \( m = 3 \) and passing through the point \( (-2, -1) \), we can use the point-slope form of a line equation:

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

where:
- \( m = 3 \) (the slope),
- \( (x_1, y_1) = (-2, -1) \) (the point it passes through).

Substitute the values into the equation:

\[
y - (-1) = 3(x - (-2))
\]

Simplify:

\[
y + 1 = 3(x + 2)
\]

Now expand the right-hand side:

\[
y + 1 = 3x + 6
\]

Subtract 1 from both sides to solve for \( y \):

\[
y = 3x + 5
\]

So, the equation of the line in slope-intercept form is:

\[
y = 3x + 5
\]

Alternatively, you can express it in general form by moving all terms to one side:

\[
3x - y = -5
\]

Would you like further details or have any questions?

Here are some related questions:
1. How do you convert between point-slope and slope-intercept forms of a line?
2. What is the general form of a linear equation?
3. How do you determine the slope of a line from two points?
4. What are the steps to graph a line given its equation?
5. How do you find the x- and y-intercepts of a line?

**Tip**: Always check if you can simplify or rearrange your final equation to suit the form requested (slope-intercept or general form).

Find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line. Slope=3; containing the point (-2, -1).

Discover how to find the equation of a line with a slope of 3 passing through the point (-2, -1). This detailed solution explores key concepts in algebra, including the point-slope form and slope-intercept form of a linear equation. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation