17) through: \( (4,-1) \), slope \( =\frac{3}{4} \)

To find the equation of a line that passes through the point \((4, -1)\) with a slope of \(\frac{3}{4}\), you can use the **point-slope form** of a linear equation. The point-slope form is given by: \[ y - y_1 = m(x - x_1) \] where: - \(m\) is the slope of the line. - \((x_1, y_1)\) is a point on the line. **Step-by-Step Solution:** 1. **Identify the given values:** - **Point \((x_1, y_1)\):** \((4, -1)\) - **Slope \(m\):** \(\frac{3}{4}\) 2. **Plug the values into the point-slope form:** \[ y - (-1) = \frac{3}{4}(x - 4) \] 3. **Simplify the equation:** \[ y + 1 = \frac{3}{4}(x - 4) \] 4. **Distribute the slope on the right-hand side:** \[ y + 1 = \frac{3}{4}x - 3 \] 5. **Isolate \(y\) to write the equation in slope-intercept form (\(y = mx + b\)):** \[ y = \frac{3}{4}x - 3 - 1 \] \[ y = \frac{3}{4}x - 4 \] **Final Answer:** \[ y = \frac{3}{4}x - 4 \]