Question

1. lola graphed the equation y = -2x + 5. could the graph below be correct? explain.

Explanation:

Step1: Recall slope-intercept form

The equation \( y = -2x + 5 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m=-2 \) and \( b = 5 \).

Step2: Analyze y - intercept

The y - intercept \( b = 5 \) means the line should cross the y - axis at \( (0,5) \). The given graph seems to cross the y - axis at a point much lower than \( y = 5 \).

Step3: Analyze slope

The slope \( m=-2=\frac{\text{rise}}{\text{run}}=\frac{-2}{1} \). This means for every 1 unit we move to the right (increase in \( x \) by 1), we move down 2 units (decrease in \( y \) by 2). The graph shown has a shallow negative slope, not a slope of - 2. A slope of - 2 should be a relatively steep downward - sloping line, while the given graph has a gentle slope.

Answer:

The graph could not be correct. The equation \( y=-2x + 5 \) has a y - intercept of 5 (so it should cross the y - axis at \( (0,5) \)) and a slope of - 2 (a relatively steep negative slope). The given graph does not match these characteristics (it has a y - intercept lower than 5 and a much shallower slope than - 2).