Question

Find the slope of the line that passes through (4,2) and (9,1)?

Answer 1

Answer:

The slope of the line is $\displaystyle -\frac{1}{5}$.

Step-by-step explanation:

We are given two coordinate points:

• $(4, 2)$
• $(9, 1)$

We are asked to find the slope of the line.

We can use the rise-over-run formula to solve for the slope of the line.

$\displaystyle \text{slope} = \frac{\text{rise}}{\text{run}}\\\\\text{slope} = \frac{y_2-y_1}{x_2-x_1}$

However, we firstly need to name our coordinate points.

In math, we can label our coordinates using the following label system:

$(x_1, y_1), (x_2, y_2)$

Therefore, we can also label our coordinates as such:

• $x_1 = 4$
• $y_1 = 2$
• $x_2 = 9$
• $y_2 = 1$

Now, we can supply these values into the formula and solve for our slope, or a better known variable, m.

$\displaystyle m = \frac{1 - 2}{9 - 4}\\\\m = \frac{-1}{5}\\\\m = -\frac{1}{5}$

Therefore, our slope is $\displaystyle -\frac{1}{5}$.

Answer 2

Answer: m= -1/5

Step-by-step explanation:

Find the Slope (4, 2) and (9, 1)

Slope is equal to the change in y over the change in x, or rise over run.

              change in y

     m =    _________

              change in x

The change in x is equal to the difference in x-coordinates (also called run), and the change in y is equal to the difference in y-coordinates (also called rise).        y₂ − y₁

     m =   _____

              x₂ − x₁

Substitute in the values of x and y into the equation to find the slope.

              1 − (2)

     m =   _____

              9 − (4)

Simplify the numerator.

                −1

     m =   _____

              9 − (4)

Simplify the denominator.

                −1

     m =   _____

                 5

Move the negative in front of the fraction.

                −1

     m =   _____

               − 5