Question

pre-algebra ic sem 1 fall 2025
analytic geometry
which statement correctly describes the slope of the linear function that is represented by the data in the table?
the slope is positive.
the slope is zero.
there is no slope.
the slope is negative.

Explanation:

Step1: Recall the slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points from the table. For example, take \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(8,8)\).

Step2: Calculate the slope

Substitute the values into the formula: \(m=\frac{8 - 0}{8 - 0}=\frac{8}{8}=1\). Wait, no, let's check another pair. Take \((x_1,y_1)=(8,8)\) and \((x_2,y_2)=( - 4,-4)\). Then \(m=\frac{-4 - 8}{-4 - 8}=\frac{-12}{-12}=1\). Wait, no, wait the \(x\) - values are \(x = 8,8,8,8,8\) (constant \(x\) - value). The formula for slope when \(x_1=x_2\) (in general \(x\) is constant) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\), and since \(x_2 - x_1=8 - 8 = 0\) (for any two points in the table as \(x\) is always \(8\)). Division by zero is undefined. But wait, looking at the table, \(x\) is constant (\(x = 8\)) for all values of \(y\). The equation of the line is \(x = 8\), which is a vertical line.

Step3: Determine the slope of a vertical line

The slope of a vertical line \(x = a\) (where \(a\) is a constant) is undefined. But looking at the options, when \(x\) is constant (for all data points \(x = 8\)), the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), and since \(x_2=x_1\) (denominator is \(0\)), there is no slope (undefined slope is described as 'there is no slope' in some basic - level terminologies).

Answer:

There is no slope.