Find an equation form for the line from Q = (1, 1) and P = (−2, 3).



To find the equation of the line passing through points \( Q(1, 1) \) and \( P(-2, 3) \), we can follow these steps:

### 1. Find the slope \( m \) of the line.
The slope formula is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Where \( (x_1, y_1) = (1, 1) \) (the coordinates of point \( Q \)) and \( (x_2, y_2) = (-2, 3) \) (the coordinates of point \( P \)).

\[
m = \frac{3 - 1}{-2 - 1} = \frac{2}{-3} = -\frac{2}{3}
\]

### 2. Use the point-slope form of the line equation.
The point-slope form is:
\[
y - y_1 = m(x - x_1)
\]
Using the slope \( m = -\frac{2}{3} \) and point \( Q(1, 1) \):
\[
y - 1 = -\frac{2}{3}(x - 1)
\]
Now, simplify the equation:
\[
y - 1 = -\frac{2}{3}x + \frac{2}{3}
\]
Add 1 to both sides:
\[
y = -\frac{2}{3}x + \frac{2}{3} + 1
\]
\[
y = -\frac{2}{3}x + \frac{5}{3}
\]

### Final equation:
\[
y = -\frac{2}{3}x + \frac{5}{3}
\]

This is the equation of the line in slope-intercept form.

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. How would you convert this line equation to standard form?
2. What is the x-intercept of this line?
3. How do you find the distance between two points in a coordinate plane?
4. What is the perpendicular slope to the line found?
5. How would you find the midpoint between \( Q \) and \( P \)?

**Tip:** In slope-intercept form, \( y = mx + b \), the value \( b \) represents the y-intercept of the line, the point where the line crosses the y-axis.

Find an equation form for the line from Q = (1, 1) and P = (−2, 3).

Learn how to find the equation of a line passing through the points Q(1, 1) and P(−2, 3). This detailed step-by-step solution covers the slope formula, point-slope form, and slope-intercept form. Suitable for students in Grades 8-10 studying algebra and coordinate geometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation