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 the points

We have two points: \((-4, -1)\) (so \( x_1 = -4, y_1 = -1 \)) and \((4, 5)\) (so \( x_2 = 4, y_2 = 5 \)).

Step3: Substitute into formula

Substitute the values into the slope formula: \( m = \frac{5 - (-1)}{4 - (-4)} \).
Simplify numerator and denominator: \( 5 - (-1) = 5 + 1 = 6 \), \( 4 - (-4) = 4 + 4 = 8 \).
So \( m = \frac{6}{8} \), and simplify the fraction by dividing numerator and denominator by 2: \( m = \frac{3}{4} \). Wait, no, wait: Wait, 6 divided by 8 is 3/4? Wait, no, wait, 5 - (-1) is 6, 4 - (-4) is 8, so 6/8 simplifies to 3/4? Wait, no, wait, 6 and 8 have a common factor of 2, so divide numerator and denominator by 2: 6÷2=3, 8÷2=4, so 3/4? Wait, no, wait, let me check again. Wait, 5 - (-1) is 6, 4 - (-4) is 8. So 6/8 reduces to 3/4? Wait, but let me check the points again. The two points are (-4, -1) and (4,5). So the change in y is 5 - (-1) = 6, change in x is 4 - (-4) = 8. So 6/8 = 3/4? Wait, no, wait, 6 divided by 8 is 3/4? Wait, no, 6 and 8: GCD is 2, so 6/8 = 3/4. Wait, but wait, maybe I made a mistake. Wait, 5 - (-1) is 6, 4 - (-4) is 8. So 6/8 simplifies to 3/4? Wait, no, 6 divided by 8 is 0.75, which is 3/4. Wait, but let me check the graph again. The y-intercept is 2, and when x is 4, y is 5. So from x=0 to x=4, y goes from 2 to 5, which is a change of 3 in y and 4 in x, so slope 3/4. Yes, that matches. So the slope is 3/4? Wait, no, wait, wait, the two points are (-4, -1) and (4,5). So the difference in y is 5 - (-1) = 6, difference in x is 4 - (-4) = 8. 6/8 = 3/4. Yes, that's correct.

Answer:

\(\frac{3}{4}\)