Question

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

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0, 15)\) (the y - intercept) and another point, say \((40, 25)\) (by looking at the grid, when \(x = 40\), \(y=25\)).

Step2: Use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\)

Let \((x_1,y_1)=(0, 15)\) and \((x_2,y_2)=(40, 25)\). Then \(m=\frac{25 - 15}{40 - 0}=\frac{10}{40}\).

Step3: Simplify the fraction

Simplify \(\frac{10}{40}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 10. So \(\frac{10\div10}{40\div10}=\frac{1}{4}\).

Answer:

\(\frac{1}{4}\)