Nolan plots the y-intercept of a line at (0, 3) on the y-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?

Question

y = 2x + 1
y = 2x + 3
y = 3x + 2
y = 3x + 5

Answer 1

To find the equation of Nolan’s line, we know two things: the y-intercept and the slope.

1. The y-intercept is at the point \( (0, 3) \), which means that when \( x = 0 \), \( y = 3 \). This tells us that the constant \( b \) in the slope-intercept form \( y = mx + b \) is 3.

2. The slope of the line is 2, which means \( m = 2 \).

Using the slope-intercept form, we can substitute in the values we have:

\[ y = mx + b \] \[ y = 2x + 3 \]

Thus, the equation representing Nolan's line is:

\[ \boxed{y = 2x + 3} \]