To find the number of units to go up after moving to the right 1 unit from the point [tex]\((0, 5)\)[/tex] on the graph of the line [tex]\(y = 2x + 5\)[/tex]:
1. Understand the Equation:
The equation of the line is in slope-intercept form [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept.
2. Identify the Slope ([tex]\(m\)[/tex]):
In the equation [tex]\(y = 2x + 5\)[/tex], the slope [tex]\(m = 2\)[/tex].
3. Interpret the Slope:
The slope of 2 can be interpreted as the ratio of the vertical change (rise) to the horizontal change (run). So a slope of 2 means that for every 1 unit you move to the right along the x-axis, the y value increases by 2 units.
4. Application to the Current Question:
Starting from the point (0, 5), moving 1 unit to the right (horizontal change) along the x-axis:
[tex]\[
\text{Horizontal change (run)} = 1
\][/tex]
According to the slope of the line, for this 1 unit horizontal change:
[tex]\[
\text{Vertical change (rise)} = 2 \text{ units}
\][/tex]
Therefore, after moving 1 unit to the right from the point (0, 5), you would go up 2 units.
Considering the choices:
(A) 0
(B) 1
(C) 5
(D) 2
Based on the interpretation and calculation of the slope:
The correct answer is [tex]\(\boxed{2}\)[/tex].
