Question

what is the slope of this line? simplify your answer and write it as a proper fraction, improper fraction, or integer. the line passes through (-5, -3) and (5, 3) on a coordinate grid.

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify the points

We have two points: \((-5, -3)\) (so \( x_1=-5, y_1 = - 3\)) and \((5, 3)\) (so \( x_2 = 5, y_2=3\)).

Step3: Substitute into the formula

Substitute the values into the slope formula: \( m=\frac{3-(-3)}{5-(-5)} \).
Simplify the numerator and denominator: \( 3 - (-3)=3 + 3 = 6 \), \( 5-(-5)=5 + 5 = 10 \).
So \( m=\frac{6}{10} \).

Step4: Simplify the fraction

Simplify \( \frac{6}{10} \) by dividing numerator and denominator by their greatest common divisor, which is 2. So \( \frac{6\div2}{10\div2}=\frac{3}{5} \)? Wait, no, wait: Wait, 3 - (-3) is 6, 5 - (-5) is 10? Wait, no, wait the points: Wait, looking at the graph, the line passes through (-5, -3) and (5, 3)? Wait, no, wait the coordinates: Wait, the x - axis and y - axis: Wait, in the graph, the point (-5, -3): x=-5, y=-3? Wait, no, wait the axes: Wait, the vertical axis is y - axis? Wait, no, wait the graph: Wait, the horizontal axis (left - right) is x - axis? Wait, no, the labels: The bottom axis is x - axis (with 8 at the bottom), and the left axis is y - axis? Wait, no, the original graph: Wait, the point (-5, -3): x=-5 (horizontal), y=-3 (vertical)? Wait, no, maybe I mixed up x and y. Wait, the standard coordinate system: (x, y), where x is horizontal, y is vertical. So the two points: Let's re - check. The first point: (-5, -3): x=-5, y=-3. The second point: (5, 3): x = 5, y=3. Then the slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{3-(-3)}{5-(-5)}=\frac{6}{10}=\frac{3}{5} \)? Wait, no, wait 3 - (-3) is 6, 5 - (-5) is 10, simplify to \( \frac{3}{5} \)? Wait, but wait, maybe I got the points wrong. Wait, looking at the graph, the line passes through the origin (0,0) as well? Wait, (-5, -3): if x=-5, y=-3, then the slope from (-5, -3) to (0,0) is \( \frac{0 - (-3)}{0 - (-5)}=\frac{3}{5} \), and from (0,0) to (5,3) is \( \frac{3-0}{5 - 0}=\frac{3}{5} \). So the slope is \( \frac{3}{5} \)? Wait, no, wait 3 - (-3) is 6, 5 - (-5) is 10, 6/10 is 3/5. Yes.

Wait, but let's do it again. \( y_2 - y_1=3-(-3)=6 \), \( x_2 - x_1=5-(-5)=10 \), so \( m = \frac{6}{10}=\frac{3}{5} \).

Answer:

\(\frac{3}{5}\)