Answer :
To determine the slope and the [tex]\( y \)[/tex]-intercept of the linear equation [tex]\( y = 5x - 4 \)[/tex], we need to compare this equation to the standard form of a linear equation, which is [tex]\( y = mx + b \)[/tex].
In the standard form [tex]\( y = mx + b \)[/tex], [tex]\( m \)[/tex] represents the slope of the line, and [tex]\( b \)[/tex] represents the [tex]\( y \)[/tex]-intercept.
Here’s the step-by-step solution:
1. Identify the slope [tex]\( m \)[/tex]:
- Compare the given equation [tex]\( y = 5x - 4 \)[/tex] with the standard form [tex]\( y = mx + b \)[/tex].
- The coefficient of [tex]\( x \)[/tex] in the given equation is 5.
- Therefore, the slope [tex]\( m \)[/tex] is [tex]\( 5 \)[/tex].
2. Identify the [tex]\( y \)[/tex]-intercept [tex]\( b \)[/tex]:
- In the given equation [tex]\( y = 5x - 4 \)[/tex], the constant term is [tex]\(-4\)[/tex].
- Therefore, the [tex]\( y \)[/tex]-intercept [tex]\( b \)[/tex] is [tex]\(-4\)[/tex].
So, the values are:
[tex]\[ \begin{aligned} m & = 5 \\ b & = -4 \end{aligned} \][/tex]
In the standard form [tex]\( y = mx + b \)[/tex], [tex]\( m \)[/tex] represents the slope of the line, and [tex]\( b \)[/tex] represents the [tex]\( y \)[/tex]-intercept.
Here’s the step-by-step solution:
1. Identify the slope [tex]\( m \)[/tex]:
- Compare the given equation [tex]\( y = 5x - 4 \)[/tex] with the standard form [tex]\( y = mx + b \)[/tex].
- The coefficient of [tex]\( x \)[/tex] in the given equation is 5.
- Therefore, the slope [tex]\( m \)[/tex] is [tex]\( 5 \)[/tex].
2. Identify the [tex]\( y \)[/tex]-intercept [tex]\( b \)[/tex]:
- In the given equation [tex]\( y = 5x - 4 \)[/tex], the constant term is [tex]\(-4\)[/tex].
- Therefore, the [tex]\( y \)[/tex]-intercept [tex]\( b \)[/tex] is [tex]\(-4\)[/tex].
So, the values are:
[tex]\[ \begin{aligned} m & = 5 \\ b & = -4 \end{aligned} \][/tex]
