Question

determine if the given graph is the graph of the function $y = -\frac{2}{5}x + 3$. enter 1 for yes. enter 2 for no.

Explanation:

Step1: Check the y-intercept

The equation \( y = -\frac{2}{5}x + 3 \) has a y-intercept at \( (0, 3) \). From the graph, the line crosses the y-axis at \( (0, 3) \), so this matches.

Step2: Check another point

Take \( x = 5 \). Plug into the equation: \( y = -\frac{2}{5}(5) + 3 = -2 + 3 = 1 \). The graph has a point at \( (5, 1) \), which matches the calculated value.

Step3: Check the slope

The slope of \( y = -\frac{2}{5}x + 3 \) is \( -\frac{2}{5} \). The change in y over change in x between \( (0, 3) \) and \( (5, 1) \) is \( \frac{1 - 3}{5 - 0} = \frac{-2}{5} = -\frac{2}{5} \), which matches the slope of the equation.

Answer:

1