91Ó°ÊÓ

The y-intercept is where the line crosses the y-axis. In other words, it's the y-value when x is 0. This is an essential concept when analyzing linear equations, especially in the slope-intercept form, which is given by \[ y = mx + b \]where \( b \) is the y-intercept. In simpler terms, if you replace \( x \) with 0 in the equation, the value you find for \( y \) will be your y-intercept.

In our original exercise, the equation is \( y = 4 \). This equation can be seen as \( y = 0x + 4 \), indicating that the y-intercept is 4.

• The x-coordinate is always \( 0 \) at the y-intercept.
• The y-coordinate is always \( b \), which represents the constant in the equation.

A horizontal line is defined by having the same y-value across all points on the line, which means there is no rise and just a run. This is why its slope is 0. These lines are parallel to the x-axis and can be represented by the equation \[ y = c \]where \( c \) is a constant.

Because the slope \( m \) of a horizontal line is 0, such lines are often encountered in everyday experiences, like looking at the horizon.

• Horizontal lines run left to right.
• The slope is always \( 0 \) because there is no vertical change.

In the given problem \( y = 4 \), it's a horizontal line at \( y = 4 \) which means the line runs parallel to the x-axis, crossing the y-axis at the point \((0, 4)\).

This point is also the y-intercept.

The slope-intercept form is a straightforward way of expressing linear equations. It is written as:\[ y = mx + b \]where \( m \) denotes the slope of the line and \( b \) is its y-intercept. This form allows for a simple understanding of how the line behaves based on its slope and where it intersects the y-axis.

Selecting equations in this form enables quick graphing and easy analysis. Suppose you compare lines; having the equation in this form makes spotting the slope's steepness and intercept location much quicker.

• The slope \( m \) indicates how steep the line is.
• The y-intercept \( b \) is where the line crosses the y-axis.

For the equation \( y = 4 \) from the exercise, you can rewrite it as \( y = 0x + 4 \) which fits the slope-intercept form where \( m = 0 \) and \( b = 4 \), letting us know it's a horizontal line with a y-intercept of 4.