Adriana writes the equation y = 2x + 4 to represent a line on a graph. Henry writes an equation that has a y-intercept that is 1 unit lower on the graph but has the same slope as Adriana’s line. Which is Henry’s equation?

Question

y = x + 4
y = 3x + 4
y = 2x + 3
y = 2x + 5

Answer 1

Adriana's equation is \( y = 2x + 4 \). This line has a slope of 2 and a y-intercept of 4.

Henry wants to write an equation with the same slope (which is 2) but a y-intercept that is 1 unit lower. Since 4 is Adriana's y-intercept, 1 unit lower would be:

\[ 4 - 1 = 3 \]

Therefore, Henry's equation will have a slope of 2 and a y-intercept of 3, which can be expressed as:

\[ y = 2x + 3 \]

So, Henry's equation is:

y = 2x + 3.