Find an equation of the line having the given slope and containing the given point. Slope \( \frac{3}{4} \); through \( (-4,4) \)

To find the equation of a line given a slope and a point, we can use the point-slope form of the equation of a line, which is: \[ y - y_1 = m(x - x_1) \] where \( m \) is the slope, and \( (x_1, y_1) \) is the point the line passes through. Given: - Slope \( m = \frac{3}{4} \) - Point \( (x_1, y_1) = (-4, 4) \) Substituting these values into the point-slope form: \[ y - 4 = \frac{3}{4}(x - (-4)) \] This simplifies to: \[ y - 4 = \frac{3}{4}(x + 4) \] Next, we can distribute the slope on the right side: \[ y - 4 = \frac{3}{4}x + \frac{3}{4} \cdot 4 \] Calculating \( \frac{3}{4} \cdot 4 \): \[ \frac{3}{4} \cdot 4 = 3 \] So the equation becomes: \[ y - 4 = \frac{3}{4}x + 3 \] Now, add 4 to both sides to solve for \( y \): \[ y = \frac{3}{4}x + 3 + 4 \] This simplifies to: \[ y = \frac{3}{4}x + 7 \] Thus, the equation of the line in slope-intercept form is: \[ \boxed{y = \frac{3}{4}x + 7} \]