Let's analyze the equation [tex]\( y = 3x \)[/tex].
In the equation of a line in slope-intercept form [tex]\( y = mx + b \)[/tex],
- [tex]\( m \)[/tex] represents the slope of the line,
- [tex]\( b \)[/tex] represents the y-intercept, which is where the line crosses the y-axis.
Given the equation [tex]\( y = 3x \)[/tex]:
- The term [tex]\( 3 \)[/tex] is the coefficient of [tex]\( x \)[/tex]. According to the slope-intercept form [tex]\( y = mx + b \)[/tex], this coefficient [tex]\( 3 \)[/tex] corresponds to [tex]\( m \)[/tex], the slope of the line.
The other terms:
- The x-intercept is the point where the line crosses the x-axis. For our given equation, it doesn't directly give us an x-intercept from the coefficient. We would need to set [tex]\( y = 0 \)[/tex] and solve for [tex]\( x \)[/tex] to find the x-intercept, but it is not directly represented by the number [tex]\( 3 \)[/tex].
- The y-intercept [tex]\( b \)[/tex] is the constant term in the equation [tex]\( y = mx + b \)[/tex]. Our given equation [tex]\( y = 3x \)[/tex] can also be written as [tex]\( y = 3x + 0 \)[/tex], indicating the y-intercept is [tex]\( 0 \)[/tex], not [tex]\( 3 \)[/tex].
Therefore, in the equation [tex]\( y = 3x \)[/tex]:
- [tex]\( 3 \)[/tex] represents the slope of the line.
So, the correct answer is: the slope.
