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

k =?
q=?


To find the equation of the line \( p: y = kx + q \) passing through the points \( A(-1, 3) \) and \( B(2, 6) \), we need to follow these steps:

### 1. Calculate the slope \( k \)
The slope \( k \) (also called the gradient) is calculated using the formula:

\[
k = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substitute the coordinates of \( A(x_1 = -1, y_1 = 3) \) and \( B(x_2 = 2, y_2 = 6) \):

\[
k = \frac{6 - 3}{2 - (-1)} = \frac{3}{3} = 1
\]

### 2. Find the intercept \( q \)
Now that we know \( k = 1 \), we can use one of the points (say \( A \)) to find the intercept \( q \). Using the equation \( y = kx + q \), substitute \( x = -1 \), \( y = 3 \), and \( k = 1 \):

\[
3 = 1(-1) + q
\]

\[
3 = -1 + q \quad \Rightarrow \quad q = 4
\]

### Final Equation
Thus, the equation of the line is:

\[
y = x + 4
\]

Would you like further details or have any questions? Here are some related questions you might find useful:

1. How can we determine if two lines are parallel?
2. What does the slope of a line represent geometrically?
3. How do you find the equation of a line given its slope and a point on the line?
4. How can you check if a point lies on a given line?
5. What happens when two points are vertically or horizontally aligned?

**Tip:** The slope of a line is a measure of how steep the line is—positive slopes rise from left to right, while negative slopes fall.

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

Learn how to find the equation of a straight line passing through points A(-1, 3) and B(2, 6) using the slope-intercept formula. This step-by-step guide covers the slope calculation and finding the y-intercept. Suitable for Grades 8-10 students.

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