To determine the slope and the [tex]\( y \)[/tex]-intercept of the linear equation [tex]\( y = 1.5x - 2 \)[/tex], let's follow these steps:
1. Identify the given equation format:
The equation [tex]\( y = 1.5x - 2 \)[/tex] is in the slope-intercept form of a linear equation, which is generally given by:
[tex]\[
y = mx + b
\][/tex]
where [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the [tex]\( y \)[/tex]-intercept.
2. Extract the slope:
From the given equation, compare it with the slope-intercept form:
[tex]\[
y = 1.5x - 2
\][/tex]
Here, the coefficient of [tex]\( x \)[/tex] corresponds to the slope [tex]\( m \)[/tex]. Therefore, the slope [tex]\( m \)[/tex] is:
[tex]\[
m = 1.5
\][/tex]
3. Extract the [tex]\( y \)[/tex]-intercept:
The term that is constant (without the variable [tex]\( x \)[/tex]) corresponds to the [tex]\( y \)[/tex]-intercept [tex]\( b \)[/tex]. In the given equation:
[tex]\[
y = 1.5x - 2
\][/tex]
The [tex]\( y \)[/tex]-intercept [tex]\( b \)[/tex] is:
[tex]\[
b = -2
\][/tex]
4. Match the findings with the given options:
We have found that the slope [tex]\( m \)[/tex] is [tex]\( 1.5 \)[/tex] and the [tex]\( y \)[/tex]-intercept [tex]\( b \)[/tex] is [tex]\( -2 \)[/tex]. Matching these with the given options:
[tex]\[
\text{A. slope } = 1.5 \text{ and } y\text{-intercept } = -2
\][/tex]
This is the correct choice.
So, the slope and the [tex]\( y \)[/tex]-intercept of the line are:
[tex]\[
\text{Slope } = 1.5 \quad \text{and} \quad y\text{-intercept} = -2
\][/tex]
Hence, the correct answer is:
[tex]\[
\text{A. slope } = 1.5 \text{ and } y\text{-intercept } = -2
\][/tex]
