To determine the slope of a line that passes through the points [tex]\((7, 10)\)[/tex] and [tex]\((7, 20)\)[/tex], we use the slope formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
First, let's identify the coordinates:
[tex]\[
(x_1, y1) = (7, 10) \quad \text{and} \quad (x_2, y_2) = (7, 20)
\][/tex]
Next, we calculate the numerator of the slope formula:
[tex]\[
y_2 - y_1 = 20 - 10 = 10
\][/tex]
Then, we calculate the denominator of the slope formula:
[tex]\[
x_2 - x_1 = 7 - 7 = 0
\][/tex]
In the slope formula:
[tex]\[
m = \frac{10}{0}
\][/tex]
We observe that the denominator is 0. Since division by zero is undefined, the slope is undefined. Therefore, the line is a vertical line and has no defined slope.
The correct statement is:
"It has no slope because [tex]\( x_2 - x_1 \)[/tex] in the formula [tex]\( m = \frac{y_2 - y_1}{x_2 - x_1} \)[/tex] is zero, and the denominator of a fraction cannot be zero."
So, the correct choice is:
“It has no slope because [tex]\( x_2 - x_1 \)[/tex] in the formula [tex]\( m = \frac{y_2 - y_1}{x_2 - x_1} \)[/tex] is zero, and the denominator of a fraction cannot be zero.”
