Question

graphing linear equations use the clues below to determine which student created each graph. type the name of the student in each white rectangle. clue #1 caleb’s graph has a positive slope and a negative y - intercept. clue #2 tierra’s graph has a negative slope and a positive y - intercept. clue #3 long’s graph has a positive slope and a positive y - intercept. clue #4 sharyah’s graph has a negative slope and a negative y - intercept.

Explanation:

Step1: Analyze Slope and Y - intercept

• Recall that the slope of a line \(y = mx + b\) is \(m\) (positive if line rises from left to right, negative if it falls) and \(y\) - intercept is \(b\) (where the line crosses the \(y\) - axis).
• For the first graph (top - most blue graph): The line falls from left to right (negative slope) and crosses the \(y\) - axis at a positive value (positive \(y\) - intercept). Match with Clue #1 (Caleb: positive slope? Wait, no, wait. Wait, first graph: let's re - check. Wait, the first graph (top) has a negative slope (falls left to right) and positive \(y\) - intercept? Wait, no, maybe I misread. Wait, Clue #1: Caleb's graph has a positive slope and negative \(y\) - intercept? No, wait the text in Clue #1: "Caleb’s graph has a positive slope and a negative y - intercept." Wait, no, the image text: "Caleb’s graph has a positive slope and a negative y - intercept." Wait, maybe I misread the graph. Wait, let's look at each graph:

Second graph (second from top): Rises from left to right (positive slope) and crosses \(y\) - axis at positive (positive \(y\) - intercept). Wait, no, let's list all clues:

Clue #1: Caleb: positive slope, negative \(y\) - intercept.

Clue #2: Tierra: negative slope, positive \(y\) - intercept.

Clue #3: Long: positive slope, positive \(y\) - intercept.

Clue #4: Sharayah: negative slope, negative \(y\) - intercept.

Now, let's analyze each graph:

1. Top graph: Line falls (negative slope) and crosses \(y\) - axis at positive (positive \(y\) - intercept) → matches Tierra (Clue #2: negative slope, positive \(y\) - intercept).

1. Second graph: Rises (positive slope) and crosses \(y\) - axis at positive (positive \(y\) - intercept) → matches Long (Clue #3: positive slope, positive \(y\) - intercept).

1. Third graph: Falls (negative slope) and crosses \(y\) - axis at negative (negative \(y\) - intercept) → matches Sharayah (Clue #4: negative slope, negative \(y\) - intercept).

1. Fourth graph: Rises (positive slope) and crosses \(y\) - axis at negative (negative \(y\) - intercept) → matches Caleb (Clue #1: positive slope, negative \(y\) - intercept).

Step2: Match Each Graph to Student

• Graph 1 (top): Negative slope, positive \(y\) - intercept → Tierra (Clue #2).
• Graph 2 (second): Positive slope, positive \(y\) - intercept → Long (Clue #3).
• Graph 3 (third): Negative slope, negative \(y\) - intercept → Sharayah (Clue #4).
• Graph 4 (bottom): Positive slope, negative \(y\) - intercept → Caleb (Clue #1).

Answer:

• Top graph: Tierra
• Second graph: Long
• Third graph: Sharayah
• Bottom graph: Caleb