Question

which is the graph of $y = 5x + 5$? three grid graphs with red lines and checkboxes, and a done button

Explanation:

Step1: Recall slope - intercept form

The equation of a line in slope - intercept form is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. For the equation \(y=5x + 5\), the slope \(m = 5\) (which is a positive slope, meaning the line rises from left to right) and the \(y\) - intercept \(b = 5\) (this means the line crosses the \(y\) - axis at the point \((0,5)\)).

Step2: Analyze the \(y\) - intercept

We need to look for the graph where the line intersects the \(y\) - axis at \(y = 5\) (i.e., the point \((0,5)\)) and has a positive slope (since \(m = 5>0\), the line should be increasing).

Looking at the three graphs:

• The first graph: The line crosses the \(y\) - axis below \(y = 5\) (maybe at \(y = 0\) or a negative value), so it does not have a \(y\) - intercept of \(5\).
• The second graph: The line crosses the \(y\) - axis at \(y = 5\) (the point \((0,5)\)) and has a positive slope (since it rises from left to right), which matches the equation \(y = 5x+5\) (slope \(m = 5\), \(y\) - intercept \(b = 5\)).
• The third graph: The line crosses the \(y\) - axis at \(y = 0\) (the origin), so it does not have a \(y\) - intercept of \(5\).

Answer:

The graph in the middle (the second graph among the three given graphs) is the graph of \(y = 5x + 5\)