Question

which graph matches the equation y=-x-3

Explanation:

Step1: Identify the slope and y-intercept

The equation \( y = -x - 3 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m=- 1 \) (the coefficient of \( x \)) and \( b = - 3 \) (the constant term).

Step2: Analyze the y - intercept

The y - intercept \( b=-3 \) means the line crosses the y - axis at the point \( (0,-3) \).

Step3: Analyze the slope

The slope \( m = - 1=\frac{-1}{1}=\frac{\text{rise}}{\text{run}} \). A negative slope means the line is decreasing (as \( x \) increases, \( y \) decreases). For a slope of - 1, for every 1 unit we move to the right (increase in \( x \) by 1), we move down 1 unit (decrease in \( y \) by 1).

Step4: Match with the graphs

We need to find the graph that has a y - intercept at \( (0,-3) \) and a negative slope (decreasing from left to right). Looking at the four graphs, the third graph (from the left) has a y - intercept at \( (0, - 3) \) and a negative slope (since as \( x \) increases, \( y \) decreases), which matches the equation \( y=-x - 3 \).

Answer:

The third graph (from the left) matches the equation \( y=-x - 3 \). (Assuming the four graphs are ordered from left to right, the one with y - intercept at \( (0,-3) \) and a negative slope)