Question

A line that includes the points (6,-6)and (10,f)has a slope of 4.What is the value of f?

Answer 1

The value of f is 10.

Step-by-step explanation:

To find the value of f, we can use the formula for slope, which is (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. Given that the slope is 4 and one point is (6, -6), we can substitute the values into the formula to find the value of f:

(f - (-6)) / (10 - 6) = 4

f + 6 = 4 * 4

f + 6 = 16

f = 16 - 6

f = 10

Answer 2

The value of f in the line passing through (6, -6) and (10, f) with a slope of 4 is 10.

What is a slope?

Slope is a measure of the steepness or incline of a line and is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. The slope (m) between two points (x₁, y₁) and (x₂, y₂) is given by the formula: m = (y₂ - y₁)(x₂ - x₁).

In this case, with the points (6, -6) and (10, f) and a given slope of 4:

4 = (f - (-6))/(10 - 6)

Solving for f:

`\[4 = \frac{{f + 6}}{4}\]`

16 = f + 6

f = 10

Therefore, the value of f is 10.