Let's match the terms to their correct definitions. Here are the definitions we need to match:
1. Slope
- This is the rate of change of a line; it describes how much [tex]\( y \)[/tex] changes for a change in [tex]\( x \)[/tex]. The description typically used is "rise over run".
2. Linear equation
- This is an equation whose graph is a straight line. A general form of this equation is [tex]\( Ax + By + C = 0 \)[/tex].
3. Slope-intercept form
- This is the specific form of a linear equation given by [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the [tex]\( y \)[/tex]-intercept.
4. [tex]\( y \)[/tex]-intercept
- This is the point where the line crosses the [tex]\( y \)[/tex]-axis. It corresponds to [tex]\( b \)[/tex] in the equation [tex]\( y = mx + b \)[/tex].
Now let's use these definitions to match the terms:
1. Slope [tex]$\square$[/tex] the rate of change of a line; change in [tex]\( y \)[/tex] over change in [tex]\( x \)[/tex]; rise over run
2. Linear equation [tex]$\square$[/tex] an equation whose graph is a line; the general form for such an equation is [tex]\( Ax + By + C = 0 \)[/tex]
3. Slope-intercept form [tex]$\square$[/tex] [tex]\( y = mx + b \)[/tex] form of a linear equation
4. [tex]\( y \)[/tex]-intercept [tex]$\square$[/tex] the point where the line crosses the [tex]\( y \)[/tex]-axis
