To write the equation of a line in slope-intercept form, we use the formula:
[tex]\[ y = mx + b \][/tex]
where [tex]\( m \)[/tex] represents the slope, and [tex]\( b \)[/tex] represents the y-intercept.
Given:
- The slope [tex]\( m \)[/tex] is 4.
- The y-intercept [tex]\( b \)[/tex] is -4.
Substituting these values into the slope-intercept form equation:
[tex]\[ y = 4x + (-4) \][/tex]
Thus, the equation of the line is:
[tex]\[ y = 4x - 4 \][/tex]
### Graphing the Line
To graph the line [tex]\( y = 4x - 4 \)[/tex] on a coordinate plane, follow these steps:
1. Plot the y-intercept: The y-intercept is the point where the line crosses the y-axis. For this equation, the y-intercept is -4. So, plot the point (0, -4).
2. Use the slope: The slope of 4 means that for every 1 unit increase in [tex]\( x \)[/tex], [tex]\( y \)[/tex] increases by 4 units. From the y-intercept (0, -4), move 1 unit to the right to [tex]\( x = 1 \)[/tex] and 4 units up to [tex]\( y = 0 \)[/tex]. This gives the point (1, 0). Plot this point.
3. Draw the line: Connect the points (0, -4) and (1, 0) with a straight line. Extend the line across the graph, making sure it continues in both directions.
Now you have the graph of the line [tex]\( y = 4x - 4 \)[/tex].
