https://file.aiquickdraw.com/mathbot/file/1726150519614fbyaqxx4.jpg

Let's break down this problem:

**a.) Write an equation of a line with the slope \( m = 4 \), which passes through the point \( (1, -1) \).**

We'll use the **point-slope form** equation for this part. The point-slope form of a line is given by:

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

Where:
- \( m \) is the slope,
- \( (x_1, y_1) \) is a point on the line.

Given \( m = 4 \) and the point \( (1, -1) \), substitute into the formula:

\[
y - (-1) = 4(x - 1)
\]

Simplifying:

\[
y + 1 = 4(x - 1)
\]

This is the equation in point-slope form.

**b.) Write the equation in slope-intercept form \( y = mx + b \).**

To convert the equation to slope-intercept form, we'll solve for \( y \):

\[
y + 1 = 4(x - 1)
\]

Distribute the 4:

\[
y + 1 = 4x - 4
\]

Subtract 1 from both sides:

\[
y = 4x - 5
\]

So the equation in slope-intercept form is:

\[
y = 4x - 5
\]

### Summary:
- **Point-slope form:** \( y + 1 = 4(x - 1) \)
- **Slope-intercept form:** \( y = 4x - 5 \)

Would you like help with graphing this equation?

---

**Relative Questions:**
1. What is the formula for the slope of a line given two points?
2. How can you determine if two lines are parallel or perpendicular based on their slopes?
3. How do you convert a standard form linear equation into slope-intercept form?
4. How does the graph of a linear equation change when the slope increases or decreases?
5. What does the y-intercept of a line tell you about its graph?

**Tip:** To graph a line easily, identify the slope (rise over run) and y-intercept first. This gives you a starting point and direction to plot!

Write an equation of a line with the slope 4, which passes through the point (1, -1). Use the point-slope form and then convert the equation to slope-intercept form.

Learn how to write the equation of a line with a slope of 4 passing through the point (1, -1). This problem covers key algebraic concepts, including the point-slope form and converting to slope-intercept form. 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