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