Answered

Nolan plots the [tex]$y$[/tex]-intercept of a line at [tex]$(0,3)$[/tex] on the [tex]$y$[/tex]-axis. He uses a slope of 2 to graph another point. He draws a line through the two points. Which equation represents Nolan's line?

A. [tex]$y = 2x + 1$[/tex]
B. [tex]$y = 2x + 3$[/tex]
C. [tex]$y = 3x + 2$[/tex]
D. [tex]$y = 3x + 5$[/tex]



Answer :

GinnyAnswer
Let's find the equation representing Nolan's line step-by-step.

1. Identifying the y-intercept and the slope:
- Nolan plots the y-intercept of the line at [tex]\( (0, 3) \)[/tex]. This means the line crosses the y-axis at [tex]\( y = 3 \)[/tex].
- The slope of the line is given as [tex]\( 2 \)[/tex].

2. Formulating the equation of the line:
- The standard form of the equation of a line is:
[tex]\[ y = mx + b \][/tex]
where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
- From the given information:
- The slope [tex]\( m = 2 \)[/tex]
- The y-intercept [tex]\( b = 3 \)[/tex]

3. Substituting the values:
- Substitute [tex]\( m = 2 \)[/tex] and [tex]\( b = 3 \)[/tex] into the standard form equation:
[tex]\[ y = 2x + 3 \][/tex]

4. Finding the correct equation among the given options:
- The correct equation that represents Nolan's line is therefore:
[tex]\[ y = 2x + 3 \][/tex]

So the correct answer is:
[tex]\[ \boxed{y = 2x + 3} \][/tex]

Other Questions