Question

b. $y = x - 5$
c. $y = -2x$
(two coordinate plane grids are shown, each with x and y axes and origin o.)

Explanation:

Step1: Analyze \( y = x - 5 \)

The equation \( y = x - 5 \) is a linear function with slope \( m = 1 \) (positive) and y - intercept \( b=-5 \). To graph it, we can find two points. When \( x = 0 \), \( y=-5 \); when \( y = 0 \), \( x = 5 \). So the line should pass through \( (0,-5) \) and \( (5,0) \), with a positive slope (going up from left to right). Looking at the left graph, we can check if it matches this description. The left graph has a coordinate system where we can plot these points.

Step2: Analyze \( y=-2x \)

The equation \( y = - 2x \) is a linear function with slope \( m=-2 \) (negative) and y - intercept \( b = 0 \) (passes through the origin). When \( x = 1 \), \( y=-2 \); when \( x=-1 \), \( y = 2 \). The line should pass through the origin and have a negative slope (going down from left to right). The right graph has a line passing through the origin with a negative slope, which matches \( y=-2x \). But for \( y=x - 5 \), the left graph's coordinate system can be used to plot the line with y - intercept at \( y=-5 \) (below the origin) and positive slope.

Answer:

For \( y = x - 5 \), the left graph; for \( y=-2x \), the right graph. (Assuming the question is to match the equations to the graphs. If the question was different, please clarify. But based on the given equations and graphs, this is the matching.)