Question

The points (p, 6) and (4, 7) fall on a line with a slope of j. Then what would the value of p end up being?

Answer 1

The slope of a line is given by the formula "rise over run," or (y2 - y1)/(x2 - x1). In this case, the rise is 7 - 6 = 1, and the run is 4 - p.

So the slope is equal to 1/(4 - p). We are told that this slope is equal to j, so we can set up the equation:

1/(4 - p) = j

To solve for p, we can multiply both sides of the equation by (4 - p) to get:

(4 - p) = j(4 - p)

Then we can simplify the left side and rearrange the terms on the right side to get:

4 - p = 4j - jp

Then we can add p to both sides to get:

4 = 4j - jp + p

Then we can combine like terms to get:

4 = (4 - p)j + p

Then we can rearrange the terms to solve for p:

p = 4 - (4 - p)j

p = 4 - 4j + pj

p = (1 - j)p + 4 - 4j

p(1 - j) = 4 - 4j

p = (4 - 4j)/(1 - j)

This is the value of p that will make the slope of the line with points (p, 6) and (4, 7) equal to j.

Answer 2

p = -5

Explanation:

`\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=(y_2-y_1)/(x_2-x_1)$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}`

Given values:

• Let (x₁, y₁) = (p, 6)
• Let (x₂, y₂) = (4, 7)
• Slope (m) = 1/9

Substitute the given points and slope into the slope formula:

`\implies (1)/(9)=(7-6)/(4-p)`

`\implies (1)/(9)=(1)/(4-p)`

Cross multiply:

`\implies 4-p=9`

Subtract 4 from both sides:

`\implies -p=5`

Divide both sides by -1:

`\implies p=-5`

Therefore, the value of p is -5.