https://file.aiquickdraw.com/mathbot/file/1727363203102n6bd9b2l.jpg

We are asked to find the equation of the straight line \( y = k \cdot x + q \), which passes through the points \( A(-1, 3) \) and \( B(2, 6) \). To do this, we need to find the values of \( k \) (the slope) and \( q \) (the y-intercept).

### Step 1: Calculate the slope \( k \)
The slope \( k \) of the line passing through two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is given by:
\[
k = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the coordinates of \( A(-1, 3) \) and \( B(2, 6) \):
\[
k = \frac{6 - 3}{2 - (-1)} = \frac{3}{3} = 1
\]

### Step 2: Find the y-intercept \( q \)
Now that we know the slope \( k = 1 \), we can use the equation of the line \( y = k \cdot x + q \) to find \( q \). We can substitute the coordinates of one of the points, say point \( A(-1, 3) \), into the equation.

Using \( A(-1, 3) \):
\[
3 = 1 \cdot (-1) + q
\]
\[
3 = -1 + q
\]
\[
q = 4
\]

### Final Equation of the Line:
The equation of the line is:
\[
y = 1 \cdot x + 4 \quad \text{or simply} \quad y = x + 4
\]

So, \( k = 1 \) and \( q = 4 \).

Would you like more details or have any questions?

Here are some related questions for further exploration:
1. How do you derive the equation of a line from different forms (e.g., point-slope)?
2. What is the geometric significance of the slope \( k \)?
3. How can you calculate the distance between two points in a plane?
4. What happens to the line equation if one of the points is on the y-axis?
5. How can the midpoint formula help when finding the center between two points?

**Tip:** Always verify the slope calculation before substituting into the line equation to avoid sign errors.

Find the equation of the straight line y = k * x + q going through the points A = [-1, 3] and B = [2, 6].

Learn how to find the equation of a line y = k * x + q passing through points A(-1, 3) and B(2, 6). This problem involves calculating the slope and determining the y-intercept using linear algebra concepts. 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