Question

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

Answer 1

To find the slope of the line passing through the points \( A(3, -2) \) and \( B(4, 12) \), we can use the formula for the slope \( m \):

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

where \((x_1, y_1)\) are the coordinates of point A and \((x_2, y_2)\) are the coordinates of point B.

Substituting the coordinates of points A and B:

- Point A: \( (x_1, y_1) = (3, -2) \)
- Point B: \( (x_2, y_2) = (4, 12) \)

Now we can plug these values into the slope formula:

\[
m = \frac{12 - (-2)}{4 - 3} = \frac{12 + 2}{4 - 3} = \frac{14}{1} = 14
\]

Thus, the slope of the line is \( \boxed{14} \).