Question

question
draw a line representing the
ise\ and a line representing the
un\ of the line. state the slope of the line in simplest form.
click twice to plot each segment.
click a segment to delete it.

Explanation:

Step1: Identify two points on the line

Let's assume the left - most point is \((x_1,y_1)=(- 10,9)\) and the right - most point is \((x_2,y_2)=(10,3)\) (by looking at the grid, we can estimate the coordinates. The x - axis and y - axis have grid lines, so we can find the change in y (rise) and change in x (run)).

Step2: Calculate the rise

The rise is the change in the y - coordinates, \(y_2 - y_1\). So \(y_2 - y_1=3 - 9=- 6\). The negative sign indicates a downward movement (since the line is decreasing from left to right).

Step3: Calculate the run

The run is the change in the x - coordinates, \(x_2 - x_1\). So \(x_2 - x_1 = 10-(-10)=20\).

Step4: Calculate the slope

The slope \(m\) of a line is given by the formula \(m=\frac{\text{rise}}{\text{run}}=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting the values of \(y_2 - y_1=-6\) and \(x_2 - x_1 = 20\), we get \(m=\frac{-6}{20}\).

Step5: Simplify the slope

We simplify \(\frac{-6}{20}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So \(\frac{-6\div2}{20\div2}=\frac{-3}{10}\).

Answer:

The slope of the line is \(\boldsymbol{-\frac{3}{10}}\)