Question

a line passes through the points in this table.

x	y
7	4
11	9
15	14
19	19

what is the slope of the line?
write your answer as an integer or simplified fraction.

Explanation:

Step1: Recall the 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: Choose two points from the table

Let's take the first two points \((7, 4)\) and \((11, 9)\). Here, \( x_1 = 7 \), \( y_1 = 4 \), \( x_2 = 11 \), \( y_2 = 9 \).

Step3: Calculate the slope

Substitute the values into the slope formula: \( m=\frac{9 - 4}{11 - 7}=\frac{5}{4} \). We can verify with other points, for example, \((11, 9)\) and \((15, 14)\): \( m=\frac{14 - 9}{15 - 11}=\frac{5}{4} \), and \((15, 14)\) and \((19, 19)\): \( m=\frac{19 - 14}{19 - 15}=\frac{5}{4} \). So the slope is consistent.

Answer:

\(\frac{5}{4}\)