Write an equation in point-slope form and slope-intercept form for: 1. passing through \( (1,9) \), slope \( =2 \) 3. passing through \( (-4,-5) \), slope \( =\frac{3}{4} \)

Certainly! Let's find the equations for both scenarios in **point-slope form** and **slope-intercept form**. --- ### 1. Line Passing Through \( (1, 9) \) with Slope \( m = 2 \) **Point-Slope Form:** The point-slope form of a line is given by: \[ y - y_1 = m(x - x_1) \] Plugging in the given point \((1, 9)\) and slope \( m = 2 \): \[ y - 9 = 2(x - 1) \] **Slope-Intercept Form:** To convert to slope-intercept form \( y = mx + b \): \[ \begin{align*} y - 9 &= 2(x - 1) \\ y - 9 &= 2x - 2 \\ y &= 2x - 2 + 9 \\ y &= 2x + 7 \end{align*} \] --- ### 2. Line Passing Through \( (-4, -5) \) with Slope \( m = \frac{3}{4} \) **Point-Slope Form:** Using the point \((-4, -5)\) and slope \( m = \frac{3}{4} \): \[ y - (-5) = \frac{3}{4}(x - (-4)) \] \[ y + 5 = \frac{3}{4}(x + 4) \] **Slope-Intercept Form:** Converting to slope-intercept form: \[ \begin{align*} y + 5 &= \frac{3}{4}(x + 4) \\ y + 5 &= \frac{3}{4}x + 3 \\ y &= \frac{3}{4}x + 3 - 5 \\ y &= \frac{3}{4}x - 2 \end{align*} \] --- ### **Summary** 1. **Passing through \( (1, 9) \), slope \( = 2 \):** - **Point-Slope Form:** \( y - 9 = 2(x - 1) \) - **Slope-Intercept Form:** \( y = 2x + 7 \) 2. **Passing through \( (-4, -5) \), slope \( = \frac{3}{4} \):** - **Point-Slope Form:** \( y + 5 = \frac{3}{4}(x + 4) \) - **Slope-Intercept Form:** \( y = \frac{3}{4}x - 2 \)