Question

given the two points on a straight-line graph,A(3,-2) and B (4,12);

B) find the equation of the line AB.

Answer 1

To find the equation of the line passing through points A(3, -2) and B(4, 12), we can follow these steps:

1. **Calculate the slope (m)** of the line using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
For points A(3, -2) and B(4, 12), we have:
- \(x_1 = 3\), \(y_1 = -2\)
- \(x_2 = 4\), \(y_2 = 12\)

Plugging in the values:
\[
m = \frac{12 - (-2)}{4 - 3} = \frac{12 + 2}{1} = \frac{14}{1} = 14
\]

2. **Use the point-slope form of the equation of a line**, which is given by:
\[
y - y_1 = m(x - x_1)
\]
We can use point A(3, -2) in this formula:
\[
y - (-2) = 14(x - 3)
\]

Simplifying this:
\[
y + 2 = 14(x - 3)
\]
\[
y + 2 = 14x - 42
\]
\[
y = 14x - 42 - 2
\]
\[
y = 14x - 44
\]

3. **Final equation**: The equation of the line AB is given by:
\[
y = 14x - 44
\]

Thus, the equation of the line through points A(3, -2) and B(4, 12) is \(y = 14x - 44\).