Find an equation for the line with the given properties.  Express the equation in​ slope-intercept form.
Containing the points Upper P equals left parenthesis negative 3 comma negative 4 right parenthesis and Upper Q equals left parenthesis negative 2 comma negative 2 right parenthesis

To find the equation of a line in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, we need to follow these steps:

### Step 1: Calculate the slope \( m \)
The formula for the slope between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \( P(-3, -4) \) and \( Q(-2, -2) \):

\[
m = \frac{-2 - (-4)}{-2 - (-3)} = \frac{-2 + 4}{-2 + 3} = \frac{2}{1} = 2
\]

So, the slope \( m = 2 \).

### Step 2: Use the point-slope form of the equation
The point-slope form is:
\[
y - y_1 = m(x - x_1)
\]
Using point \( P(-3, -4) \) and the slope \( m = 2 \), we substitute into the point-slope form:
\[
y - (-4) = 2(x - (-3))
\]
Simplifying:
\[
y + 4 = 2(x + 3)
\]

### Step 3: Simplify to slope-intercept form
Now expand and simplify the equation to get it into the form \( y = mx + b \):
\[
y + 4 = 2x + 6
\]
\[
y = 2x + 6 - 4
\]
\[
y = 2x + 2
\]

### Final Answer:
The equation of the line in slope-intercept form is:
\[
y = 2x + 2
\]

Would you like more details on any of the steps?

Here are 5 related questions for further exploration:
1. How do you find the slope when both points have the same x-coordinate?
2. Can you derive the equation if given two points with a vertical or horizontal line?
3. How can we convert from slope-intercept form to standard form?
4. What happens to the equation of a line when its slope is zero?
5. How does the slope relate to the angles a line makes with the x-axis?

**Tip:** To check your work, plug the coordinates of one of the given points back into the equation and verify that both sides are equal.

Find an equation for the line with the given properties. Express the equation in slope-intercept form. Containing the points P = (-3, -4) and Q = (-2, -2).

Learn how to find the equation of a line passing through the points (-3, -4) and (-2, -2) in slope-intercept form. This tutorial covers essential algebraic concepts like the slope formula, point-slope form, and slope-intercept form. Suitable for Grades 8-10 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation