Question

Find the value of k so that a line passing through (k, k – 3) and (–2, 4) has a slope of 1/4.

A. –3

B. 2

C. 5

D. 10

Answer 1

Do you know how to find the slope of a line given two points on the line?

Answer 2

No...

Answer 3

use this eq
\[(y2-y1)=m(x2-x1)\]
here
y2=4
y1=k-3
x2=-2
x1=k
and
m=slope=1/4
put values and ans=10 option C.

Answer 4

For points \((x_1, y_1)\) and \((x_2, y_2) \), the slope of the line that passes through the points is

\(m = \dfrac{y_2 - y_1}{x _2 - x_1} \)

Answer 5

If you look at the slope formula above, finding the slope is simple.
First you subtract the y-coordinates of the 2 points.
Then you subtract the x-coordinates of the two points.
Then you divide the difference in y by the difference in x.

You are given two points and a slope.

Let's use the slope formula with your info.

Answer 6

\(m = \dfrac{y_2 - y_1}{x_2 - x_1} \)

\(\dfrac{1}{4} = \dfrac{(k - 3) - (4)}{(k) - (-2)} \)

Do you understand the line above?

Answer 7

Uhhh....not really. I'm sorry.

Answer 8

I used the formula for the slope. I wrote the slope formula just above the last line.
The left side is m, slope.
Your slope is given as 1/4, so we have 1/4 on the left side.
Ok?

Answer 9

Okay

Answer 10

On the right side, we have a fraction.
In the numerator, we a subtracting the y-values of the two points.
In the denominator, we a subtracting the x-values of the two points.
That's how we find a slope.

Answer 11

Thank you!

Answer 12

Now you need to simplify the equation we have and solve it for k.

Answer 13

\(\dfrac{1}{4} = \dfrac{(k - 3) - (4)}{(k) - (-2)}\)

Step 1. Get rid of parentheses:

\(\dfrac{1}{4} = \dfrac{k - 3 - 4}{k +2}\)

Step 2. Combine like terms:

\(\dfrac{1}{4} = \dfrac{k - 7}{k +2}\)

Step 3.Cross multiply

(1)(k + 2) = 4(k - 7)

k + 2 = 4k - 28

-3k = -30

k = 10

Answer 14

Now let's check
For k = 10, the point is (k, k - 3) = (10, 10 - 3) = (10, 7)
Does the line through (10, 7) and (-2, 4) have a slope of 1/4?

\(m = \dfrac{7 - 4}{10 - (-2)} = \dfrac{3}{10 + 2} = \dfrac{3}{12} = \dfrac{1}{4} \)

The slope is 1/4, so our answer is correct.

Answer 15

Thank you so much!!!!

Answer 16

You're welcome.