Question

which graph has x - intercept = - 2 and y - intercept = - 2

Explanation:

Step1: Recall intercept - definition

The x - intercept is the point where the line crosses the x - axis (y = 0), and the y - intercept is the point where the line crosses the y - axis (x = 0). Given x - intercept=-2 (point (-2,0)) and y - intercept=-2 (point (0, - 2)).

Step2: Find 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, - 2), we have \(m=\frac{-2 - 0}{0-(-2)}=\frac{-2}{2}=-1\).

Step3: Analyze the graphs

A line with a negative slope and x - intercept at x=-2 and y - intercept at y = - 2 will start from the upper left and go to the lower right and cross the x - axis at x=-2 and the y - axis at y=-2.

Answer:

The graph that has a line starting from the upper - left, crossing the x - axis at x = - 2 and the y - axis at y=-2 (usually the second graph from the left among the given options if the standard orientation of graphs is assumed). Without specific labels for the graphs, it's described by its intercept and slope characteristics.