To identify the slope and intercept of the given linear equation [tex]\( y = \frac{3}{4} x - 2 \)[/tex], let's break it down step-by-step.
Let's start with the general form of a linear equation in slope-intercept form:
[tex]\[ y = mx + b \][/tex]
Here:
- [tex]\( m \)[/tex] is the slope of the line.
- [tex]\( b \)[/tex] is the y-intercept, the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex].
Given equation:
[tex]\[ y = \frac{3}{4} x - 2 \][/tex]
Comparing this with the general form [tex]\( y = mx + b \)[/tex]:
- The coefficient of [tex]\( x \)[/tex] is [tex]\(\frac{3}{4}\)[/tex], which represents the slope ([tex]\(m\)[/tex]).
- The constant term [tex]\(-2\)[/tex] represents the intercept ([tex]\(b\)[/tex]).
So, from the equation [tex]\( y = \frac{3}{4} x - 2 \)[/tex]:
- Slope [tex]\( m = \frac{3}{4} \)[/tex]
- Intercept [tex]\( b = -2 \)[/tex]
The correct answer is:
A. Slope: [tex]\(3 / 4\)[/tex]; intercept: [tex]\( -2 \)[/tex]
