Question

question 3 (1 point)
what is the slope of the line pictured in the standard (x,y) coordinate plane below that passes through (1,3) and (5,5) in the standard (x,y) coordinate plane?
image of a line in a coordinate plane
a. -2
b. -\frac{2}{5}
c. \frac{1}{5}
d. \frac{1}{2}
e. \frac{5}{3}
multiple choice options with some selected

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

Here, \((x_1, y_1)=(1, 3)\) and \((x_2, y_2)=(5, 5)\).

Step3: Substitute into formula

Substitute the values into the slope formula: \( m=\frac{5 - 3}{5 - 1} \).

Step4: Simplify the expression

Simplify the numerator and denominator: \( 5 - 3 = 2 \) and \( 5 - 1 = 4 \), so \( m=\frac{2}{4}=\frac{1}{2} \).

Answer:

D. \(\frac{1}{2}\)