To determine the correct statement about the line that passes through the points [tex]\((7, 10)\)[/tex] and [tex]\((7, 20)\)[/tex], we'll need to analyze the formula for the slope of a line.
The slope [tex]\(m\)[/tex] of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by the formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Let's substitute the given points into the formula:
- [tex]\(x_1 = 7\)[/tex], [tex]\(y_1 = 10\)[/tex]
- [tex]\(x_2 = 7\)[/tex], [tex]\(y_2 = 20\)[/tex]
We get:
[tex]\[ x_2 - x_1 = 7 - 7 = 0 \][/tex]
The denominator of our slope formula becomes zero. Division by zero is undefined in mathematics, which means the slope [tex]\(m\)[/tex] cannot be calculated in this case. When the denominator of this formula is zero, it implies that the line is vertical.
A vertical line has no defined slope because the value is undefined. Hence, 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."
