Question

The slope of the line that passes through points (-6, w) and (-10, 4) is 1/8. What is the value of w? A. 36 B. 34 C. 9/2 D. 1/2 E. Answer not given​

Answer 1

Answer:

$w=\frac92$

Step-by-step explanation:

Let's remember that the slope of a line measures the ratio of the variation in y over the variation in x. Let's plug the numbers we have and see what we get

$m= \frac {\Delta y}{\Delta x}; \frac18 = \frac{w-4}{-6-(-10)}\rightarrow\\\frac18 = \frac{w-4}{4}\rightarrow 2w-8=1 \rightarrow w=\frac92$

Answer 2

Answer:

C. $\frac{9}{2}$

Step-by-step explanation:

Hi there!

We are given the points (-6, w) and (-10,4), and that the slope that passes between these two lines is 1/8

We want to find the value of w

We can do that by plugging in our given values into the equation $\frac{y_2-y_1}{x_2-x_1}=m$, where $(x_1, y_1)$ and $(x_2, y_2)$ are points, and m is the slope

We have everything we need to solve the equation, let's just label their values to avoid any confusion.

$x_1=-6\\y_1=w\\x_2=-10\\y_2=4\\m=\frac{1}{8}$

Now plug all of these values into the formula (remember: we have NEGATIVE values, and the formula contains SUBTRACTION)

$\frac{y_2-y_1}{x_2-x_1}=m$

$\frac{4-w}{-10--6}=\frac{1}{8}$

Simplify:

$\frac{4-w}{-10+6}=\frac{1}{8}$

Add the values together

$\frac{4-w}{-4}=\frac{1}{8}$

Now we can cross multiply; multiply -4 by 1 and (4-w) by 8

-4=32-8w

Subtract 32 from both sides

-36=-8w

Divide both sides by 8

w=$\frac{9}{2}$

The answer is C

Hope this helps!