Sure! Let's graph the equation of the line: [tex]\( Y = 4X + 5 \)[/tex].
### Step-by-Step Solution:
1. Identify the slope and y-intercept:
- The given equation is in the slope-intercept form, [tex]\( Y = mX + b \)[/tex], where [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the y-intercept.
- Here, [tex]\( m = 4 \)[/tex] (slope) and [tex]\( b = 5 \)[/tex] (y-intercept).
2. Plot the y-intercept:
- The y-intercept is the point where the line crosses the y-axis. This occurs when [tex]\( X = 0 \)[/tex].
- For [tex]\( X = 0 \)[/tex], [tex]\( Y = 4(0) + 5 = 5 \)[/tex].
- So, one point on the graph is [tex]\((0, 5)\)[/tex].
3. Use the slope to find another point:
- The slope [tex]\( m = 4 \)[/tex] means that for every unit increase in [tex]\( X \)[/tex], [tex]\( Y \)[/tex] increases by 4 units.
- Starting from [tex]\((0, 5)\)[/tex], if you increase [tex]\( X \)[/tex] by 1, [tex]\( Y \)[/tex] will increase by 4 units.
- So, moving 1 unit to the right along the x-axis from [tex]\((0, 5)\)[/tex], the new point is [tex]\((1, 9)\)[/tex]:
[tex]\[
Y = 4(1) + 5 = 9
\][/tex]
4. Plot more points if desired:
- To make our line more accurate, we can find more points by using different values of [tex]\( X \)[/tex].
- If [tex]\( X = -1 \)[/tex]:
[tex]\[
Y = 4(-1) + 5 = 1
\][/tex]
So, another point is [tex]\((-1, 1)\)[/tex].
- If [tex]\( X = 2 \)[/tex]:
[tex]\[
Y = 4(2) + 5 = 13
\][/tex]
So, another point is [tex]\((2, 13)\)[/tex].
5. Draw the line:
- Plot the points [tex]\((0, 5)\)[/tex], [tex]\((1, 9)\)[/tex], [tex]\((-1, 1)\)[/tex], and [tex]\((2, 13)\)[/tex] on the coordinate plane.
- Draw a straight line through these points, extending the line in both directions.
### Summary:
1. Plot the y-intercept point [tex]\((0, 5)\)[/tex].
2. Using the slope, plot additional points such as [tex]\((1, 9)\)[/tex], [tex]\((-1, 1)\)[/tex], and [tex]\((2, 13)\)[/tex].
3. Draw a straight line through these points.
This line represents the graph of the equation [tex]\( Y = 4X + 5 \)[/tex].
