Question

Graph the line with the slope of 3/4 fourths that passes through point -3, and -5

Answer 1

To graph the line with a slope of \( \frac{3}{4} \) that passes through the point \((-3, -5)\), follow these steps:

1. **Identify the slope and point**: The slope \( m = \frac{3}{4} \) and the point is \( (-3, -5) \).

2. **Use the point-slope form of the equation of a line**:
\[
y - y_1 = m(x - x_1)
\]
Here, \( (x_1, y_1) = (-3, -5) \) and \( m = \frac{3}{4} \).

3. **Substitute the values into the equation**:
\[
y - (-5) = \frac{3}{4}(x - (-3))
\]
\[
y + 5 = \frac{3}{4}(x + 3)
\]

4. **Simplify the equation**:
\[
y + 5 = \frac{3}{4}x + \frac{3}{4} \cdot 3
\]
\[
y + 5 = \frac{3}{4}x + \frac{9}{4}
\]
\[
y = \frac{3}{4}x + \frac{9}{4} - 5
\]
To subtract 5, convert 5 into quarters:
\[
y = \frac{3}{4}x + \frac{9}{4} - \frac{20}{4}
\]
\[
y = \frac{3}{4}x - \frac{11}{4}
\]

5. **Graphing the line**:
- Start at the point \((-3, -5)\).
- From this point, use the slope \( \frac{3}{4} \) to find another point. This means for every 4 units you move to the right (positive direction), you will move up 3 units.
- Move from \((-3, -5)\) to the right 4 units to \((1, -5)\) and then up 3 units to \((1, -2)\). This gives you another point \((1, -2)\).
- Connect the points \((-3, -5)\) and \((1, -2)\) to draw the line.

6. **Final Line Equation**: The equation of the line is \( y = \frac{3}{4}x - \frac{11}{4} \).

By following these steps, you can accurately graph the line on a coordinate plane.