which of the following is the graph of this function rule? y = -4 + 3x

Answer:

The first graph.

Explanation:

Step1: Identify the slope - intercept form.

The equation $y=-4 + 3x$ is in slope - intercept form $y=mx + b$, where $m = 3$ (slope) and $b=-4$ (y - intercept).

Step2: Analyze the y - intercept.

The y - intercept $b=-4$ means the line crosses the y - axis at the point $(0,-4)$. The first graph has a line that crosses the y - axis at $y =-4$.

Step3: Analyze the slope.

The slope $m = 3=\frac{3}{1}$, which means for every 1 unit increase in $x$, $y$ increases by 3 units. The first graph has a positive - sloping line consistent with a slope of 3.