Question

what is the slope of this line? simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Recall slope formula

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

Step2: Identify two points

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

Step3: Substitute into formula

Substitute into \( m=\frac{y_2 - y_1}{x_2 - x_1} \): \( m=\frac{3 - (-3)}{5 - (-5)}=\frac{3 + 3}{5 + 5}=\frac{6}{10}=\frac{3}{5} \)? Wait, no, wait: Wait, \( 3 - (-3)=6 \), \( 5 - (-5)=10 \), simplify \( \frac{6}{10}=\frac{3}{5} \)? Wait, no, wait, actually, let's check again. Wait, \( (5,3) \) and \( (-5,-3) \): \( y_2 - y_1 = 3 - (-3)=6 \), \( x_2 - x_1 = 5 - (-5)=10 \), so \( \frac{6}{10}=\frac{3}{5} \)? Wait, no, wait, maybe I made a mistake. Wait, no, the line passes through the origin? Wait, the origin is (0,0). Let's use (0,0) and (5,3). Then \( m=\frac{3 - 0}{5 - 0}=\frac{3}{5} \)? Wait, no, ( - 5, - 3) and (5,3): the difference in y is 3 - (-3)=6, difference in x is 5 - (-5)=10, so 6/10=3/5. Wait, but also, from (0,0) to (5,3), slope is 3/5. Wait, but let's check again. Wait, the two points given are (-5, -3) and (5, 3). So \( y_2 - y_1 = 3 - (-3)=6 \), \( x_2 - x_1 = 5 - (-5)=10 \), so \( \frac{6}{10}=\frac{3}{5} \). Wait, but wait, maybe I messed up the points. Wait, the graph: ( - 5, - 3) and (5, 3). So the slope is \( \frac{3 - (-3)}{5 - (-5)}=\frac{6}{10}=\frac{3}{5} \)? Wait, no, wait, 3 - (-3) is 6, 5 - (-5) is 10, 6 divided by 10 is 3/5. Wait, but let's check with (0,0) and (5,3): 3 - 0 = 3, 5 - 0 = 5, so 3/5. Yes, same result. So the slope is \( \frac{3}{5} \)? Wait, no, wait, wait, no, wait: Wait, 3 - (-3) is 6, 5 - (-5) is 10, 6/10 reduces to 3/5. Yes.

Wait, no, wait, I think I made a mistake earlier. Wait, the two points are (-5, -3) and (5, 3). So the change in y is 3 - (-3) = 6, change in x is 5 - (-5) = 10, so slope is 6/10 = 3/5. Yes.

Answer:

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