Question

Graph the line with the given point and slope.
The line through ​(1​,1​) with slope five fourths

Answer 1

To graph the line through the point \((1, 1)\) with a slope of \(\frac{5}{4}\), follow these steps:

1. **Identify the point**: Start by plotting the point \((1, 1)\) on the coordinate plane.

2. **Understand the slope**: The slope of \(\frac{5}{4}\) means that for every 4 units you move to the right (in the positive x-direction), you will move up 5 units (in the positive y-direction).

3. **Plot another point using the slope**:
- From the point \((1, 1)\), move 4 units to the right to \(x = 1 + 4 = 5\).
- Then move up 5 units to \(y = 1 + 5 = 6\).
- This gives you a new point at \((5, 6)\).

4. **Draw the line**: After plotting the two points \((1, 1)\) and \((5, 6)\), you can draw a straight line through these points.

5. **Extend the line**: Extend the line in both directions and place arrows at the ends to indicate that it continues indefinitely.

You can also write the equation of the line in slope-intercept form \((y = mx + b)\):

- Using the point-slope formula: \(y - y_1 = m(x - x_1)\)
- Plug in \(m = \frac{5}{4}\) and the point \((1, 1)\):
\[
y - 1 = \frac{5}{4}(x - 1)
\]
- Simplify this into slope-intercept form:
\[
y - 1 = \frac{5}{4}x - \frac{5}{4}
\]
\[
y = \frac{5}{4}x - \frac{1}{4}
\]

Now, you have the required graph and the equation.