Question

use the equation to answer the questions below.
x = 1
what is the y-intercept?
what is the slope?
skill code: 313003

Explanation:

For the y - intercept:

Step1: Analyze the equation \(x = 1\)

The equation \(x=1\) represents a vertical line. A vertical line is of the form \(x = a\) (where \(a\) is a constant). For a vertical line, it is parallel to the \(y\) - axis. The \(y\) - intercept is the point where the line crosses the \(y\) - axis, which occurs when \(x = 0\). But for the line \(x=1\), \(x\) is always equal to 1 and never equal to 0. So, there is no point on the line \(x = 1\) where \(x=0\), which means the \(y\) - intercept does not exist.

Step2: Conclusion for y - intercept

Since the line \(x = 1\) (vertical line) never intersects the \(y\) - axis (as it requires \(x = 0\) to intersect the \(y\) - axis), the \(y\) - intercept doesn't exist.

For the slope:

Step1: Recall the formula for slope

The slope \(m\) of a line is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\) for two points \((x_1,y_1)\) and \((x_2,y_2)\) on the line. For the line \(x = 1\), let's take two points on the line, say \((1,0)\) and \((1,1)\). Then \(x_1=x_2 = 1\), so \(x_2 - x_1=1 - 1=0\).

Step2: Calculate the slope

If we try to calculate the slope using the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), we get \(m=\frac{1 - 0}{1 - 1}=\frac{1}{0}\). Division by zero is undefined. So, the slope of a vertical line (like \(x = 1\)) is undefined.

Answer:

(y - intercept):
Doesn't Exist