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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]

Sagot :

GinnyAnsweridn
To determine the correct equation that represents Nolan's line, we need to recall the equation of a line in slope-intercept form, which is given by:

[tex]\[ y = mx + b \][/tex]

Here, [tex]\( m \)[/tex] represents the slope of the line, and [tex]\( b \)[/tex] represents the y-intercept of the line.

Based on the information given:

1. The y-intercept of the line is at [tex]\( (0, 3) \)[/tex]. This means that when [tex]\( x = 0 \)[/tex], [tex]\( y = 3 \)[/tex]. Therefore, [tex]\( b = 3 \)[/tex].

2. The slope of the line is 2. This means the line rises 2 units for every 1 unit it runs horizontally. Therefore, [tex]\( m = 2 \)[/tex].

Substituting the values of [tex]\( m \)[/tex] and [tex]\( b \)[/tex] into the slope-intercept form, we get:

[tex]\[ y = 2x + 3 \][/tex]

Therefore, the equation that represents Nolan's line is:

[tex]\[ y = 2x + 3 \][/tex]

Among the given options:
- [tex]\( y = 2x + 1 \)[/tex]
- [tex]\( y = 2x + 3 \)[/tex]
- [tex]\( y = 3x + 2 \)[/tex]
- [tex]\( y = 3x + 5 \)[/tex]

The correct equation is:

[tex]\[ y = 2x + 3 \][/tex]
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