Graph the line with the given slope $$ m $$ and $$ y $$-intercept $$ b $$. $$ m=\frac{1}{5}, \quad b=-5 $$

Question

UpStudy AI · Accepted Answer

To graph the line with the given slope $$ m = \frac{1}{5} $$ and $$ y $$-intercept $$ b = -5 $$, we can follow these steps:

1. **Identify the y-intercept**: The y-intercept is the point where the line crosses the y-axis. For $$ b = -5 $$, this point is $$ (0, -5) $$.

2. **Use the slope to find another point**: The slope $$ m = \frac{1}{5} $$ means that for every 1 unit you move up (rise), you move 5 units to the right (run). Starting from the y-intercept $$ (0, -5) $$:
   - Move up 1 unit to $$ y = -4 $$ (from -5 to -4).
   - Move 5 units to the right to $$ x = 5 $$.
   - This gives us the point $$ (5, -4) $$.

3. **Plot the points**: Now we have two points to plot:
   - Point 1: $$ (0, -5) $$
   - Point 2: $$ (5, -4) $$

4. **Draw the line**: Connect these two points with a straight line, extending it in both directions.

The equation of the line can also be expressed in slope-intercept form as:
$$
y = \frac{1}{5}x - 5
$$

This line will have a gentle upward slope due to the positive slope value.
To graph the line with slope $$ m = \frac{1}{5} $$ and y-intercept $$ b = -5 $$, plot the point $$ (0, -5) $$ and another point using the slope (e.g., $$ (5, -4) $$), then draw a straight line through these points.

Graph the line with the given slope \( m \) and \( y \)-intercept \( b \). \( m=\frac{1}{5}, \quad b=-5 \)

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Algebra Questions