Question

54 linear function k has a zero of -2 and a y - intercept of 6. which graph best represents k?

Explanation:

Step1: Recall linear - function properties

A zero of a linear function is the x - value when y = 0. So, the function k has a point (-2,0). The y - intercept is the y - value when x = 0, so the function k has a point (0,6).

Step2: Calculate the slope

The slope m of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using the points (-2,0) and (0,6), we have \(x_1=-2,y_1 = 0,x_2=0,y_2 = 6\). Then \(m=\frac{6 - 0}{0-(-2)}=\frac{6}{2}=3\). Since the slope is positive, the line is increasing from left - to - right.

Step3: Analyze the graphs

Graph H has a positive slope, passes through the points (-2,0) and (0,6) approximately. Graph F has a negative slope. Graph G has a very steep positive slope (not 3). Graph J has a negative slope.

Answer:

H