Question

Find the slope of the line that passes through the points

Answer 1

The slope of the line through A(2,3) and B(4,7) is 2, indicating a positive change of 2 in y per unit x.

The slope of a line passing through two points, (x1, y1) and (x2, y2), can be found using the formula:

`\[ \text{Slope} (m) = (y2 - y1)/(x2 - x1) \]`

Let's apply this formula to find the slope of the line passing through points A(2,3) and B(4,7):

`\[ m = (7 - 3)/(4 - 2) \]`

`\[ m = (4)/(2) \]`

m = 2

Therefore, the slope of the line passing through points A(2,3) and B(4,7) is 2.

Interpretation:

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x). In this case, a slope of 2 means that for every unit increase in x, the corresponding y-value increases by 2 units. This positive slope indicates a positively sloped line, meaning that as x increases, y also increases.

Graphically, the line rises at a 45-degree angle from left to right, reflecting the positive slope between points A and B on the coordinate plane. This interpretation provides insight into the relationship between the two points and the direction of the line.

Question:

Find the slope of the line passing through the points A(2,3) and B(4,7)