Question

Use an equation to find the value of k so that the line that passes through the given points has the given slope. (

4,−4), (k,−1); slope=34

Answer 1

By using the slope formula, the value of ‘k’ that ensures the line through (4, -4) and (k, -1) has a slope of ⅔ is determined to be 12.

Step-by-step explanation:

Finding the Value of ‘k’ for a Line with a Given Slope

To find the value of ‘k’ so that the line passing through the points (4, -4) and (k, -1) has a slope of ⅔, use the slope formula which is ⅔ = (y2 - y1) / (x2 - x1). In this case, (x1, y1) is (4, -4) and (x2, y2) is (k, -1), therefore:

(-1 - (-4)) / (k - 4) = ⅔

3 / (k - 4) = ⅔

Multiply both sides by (k - 4) to get:

3 = (⅔)(k - 4)

Now divide both sides by ⅔ to isolate ‘k’:

3 / (⅔) = k - 4

Add 4 to both sides to get the value of ‘k’:

3 / (⅔) + 4 = k

After calculating, we get:

k = 12