Question

2 the graph of a linear function is shown on the grid. which function is best represented by this graph? f ( g(x)=6x - 4 ) g ( g(x)=4x-\frac{2}{3} ) h ( g(x)=-\frac{3}{2}x + 6 ) j ( g(x)=-\frac{2}{3}x + 4 )

Explanation:

Step1: Recall slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Determine y - intercept

The line crosses the y - axis at $y = 6$, so $b = 6$.

Step3: Calculate the slope

Using two points on the line, say $(0,6)$ and $(4,0)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 6}{4-0}=-\frac{6}{4}=-\frac{3}{2}$.

Step4: Find the equation

The equation of the line is $y=-\frac{3}{2}x + 6$, so the function is $g(x)=-\frac{3}{2}x + 6$.

Answer:

H. $g(x)=-\frac{3}{2}x + 6$