Question

which graph matches the equation $y + 6 = \frac{3}{4}(x + 4)$? graph with points (-4, -6), (0, -3), (4, 0) and a line passing through them, along with a coordinate grid from -10 to 10 on both axes

Explanation:

Step1: Identify the form of the equation

The given equation is \( y + 6=\frac{3}{4}(x + 4) \), which is in the point - slope form \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(- 4,-6) \) and the slope \( m = \frac{3}{4} \).

Step2: Analyze the graph

We can check if the point \( (-4,-6) \) lies on the line in the graph. Also, we can find the \( y \) - intercept by setting \( x = 0 \) in the equation:
Substitute \( x = 0 \) into \( y+6=\frac{3}{4}(x + 4) \)
\( y+6=\frac{3}{4}(0 + 4) \)
\( y+6=\frac{3}{4}\times4 \)
\( y + 6=3 \)
\( y=3 - 6=-3 \)
So the \( y \) - intercept is \( (0,-3) \), and the line passes through \( (-4,-6) \), \( (0,-3) \) and \( (4,0) \) as shown in the given graph.

Answer:

The graph (the one with the line passing through \((-4,-6)\), \((0, - 3)\) and \((4,0)\)) matches the equation \(y + 6=\frac{3}{4}(x + 4)\).