Question

The slope between the points (4,2) and (1. p) is 4. Find p and write the

equation of the line that has these points in point slope form.
Hint
P-2
D-10
equation of the line: \y - y1) = m(- X1)
Y1
m-
X1

Answer 1

`slope = (y_2 - y_1)/(x_2-x_1)\\\\4 = (p-2)/(1-4) \\\\4 * -3 = p -2\\\\-12 + 2 = p \\\\p = -10 \\\\Equation \ of \ line : \\\\(y -y_1) = m(x - x_1)\\\\y - 2= 4(x-4)\\\\y - 2 = 4x -16\\\\y = 4x -14`

Answer 2

Hi there! The slope formula is:

`\large \boxed{m = (y_2 - y_1)/(x_2 - x_1) }`

We know that the slope is 4 but we are missing the value of p. (Define m = slope)

What we have now are:

• two ordered pairs (4,2) and (1,p)
• value of slope = 4

We are going to substitute these values and solve the equation for p-term.

`\large{4 = (2 - p)/(4 - 1) } \\ \large{4 = (2 - p)/(3) } \\ \large{4(3) = (2 - p)/(3) (3)} \\ \large{12 = 2 - p} \\ \large{p = 2 - 12 \longrightarrow \boxed{p = - 10}}`

Hence, the value of p is -10.

Next, we have to write the equation of a line in point-slope form. The point-slope form is:

`\large \boxed{y - y_1 = m(x - x_1)}`

Define that (x1, y1) = ordered pairs

Since we have two given points, we can either use the first point or second point. Both work.

First Point

For our first ordered pairs (4,2), substitute x1 = 4 and y1 = 2 in the equation.

`\large{y - 2 = 4(x - 4)}`

Hence, the equation of a line in point-slope form as in (4,2) is y-2=4(x-4)

Second Point

For our second ordered pairs (1,p), we know that p = -10 from the equation that we solved. Therefore (1,p) = (1,-10). Substitute x1 = 1 and y1 = -10 in the equation.

`\large{y - ( - 10) = 4(x - 1)} \\ \large{y + 10 = 4(x - 1)}`

Hence, the equation of a line in point-slope form as in (1,-10) is y+10 = 4(x-1)

Answer

• The value of p is -10 (p = -10)
• y - 2 = 4(x-4) —> use (4,2) to form an equation.
• y + 10 = 4(x-1) —> use (1,-10) to form an an equation.

Both equations work for point-slope form.

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Hope this helps, and Happy Learning! :)