Question

1 2 3 a $y = -x$ b $y = x + 1$ c $y = x - 1$ d $y = x - 4$ e $y = x + 4$ f $y = x$ try again!

Explanation:

To solve this, we analyze each graph:

Graph 1:

• Passes through the origin \((0,0)\) and has a slope of \(1\) (since it's a line with equal rise and run, and positive slope). The equation of a line with slope \(m\) and \(y\)-intercept \(b\) is \(y = mx + b\). Here, \(m = 1\) and \(b = 0\), so the equation is \(y = x\), which corresponds to option F.

Graph 2:

• Let's find two points. From the graph, when \(x=-4\), \(y = 0\) (since it crosses the \(x\)-axis at \((-4,0)\)) and when \(x = 0\), \(y=4\) (crosses the \(y\)-axis at \((0,4)\)). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{4 - 0}{0 - (-4)}=\frac{4}{4}=1\). Using the slope-intercept form \(y=mx + b\), with \(m = 1\) and \(b = 4\) (from the \(y\)-intercept \((0,4)\)), the equation is \(y=x + 4\), which corresponds to option E.

Graph 3:

• Passes through the origin \((0,0)\) and has a negative slope (since it goes down from left to right). The slope \(m=-1\) (equal rise and run, but negative). Using \(y=mx + b\) with \(m=-1\) and \(b = 0\), the equation is \(y=-x\), which corresponds to option A.

Final Answers:

• Graph 1: F. \(y = x\)
• Graph 2: E. \(y = x + 4\)
• Graph 3: A. \(y=-x\)

Answer:

To solve this, we analyze each graph:

Graph 1:

• Passes through the origin \((0,0)\) and has a slope of \(1\) (since it's a line with equal rise and run, and positive slope). The equation of a line with slope \(m\) and \(y\)-intercept \(b\) is \(y = mx + b\). Here, \(m = 1\) and \(b = 0\), so the equation is \(y = x\), which corresponds to option F.

Graph 2:

• Let's find two points. From the graph, when \(x=-4\), \(y = 0\) (since it crosses the \(x\)-axis at \((-4,0)\)) and when \(x = 0\), \(y=4\) (crosses the \(y\)-axis at \((0,4)\)). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{4 - 0}{0 - (-4)}=\frac{4}{4}=1\). Using the slope-intercept form \(y=mx + b\), with \(m = 1\) and \(b = 4\) (from the \(y\)-intercept \((0,4)\)), the equation is \(y=x + 4\), which corresponds to option E.

Graph 3:

• Passes through the origin \((0,0)\) and has a negative slope (since it goes down from left to right). The slope \(m=-1\) (equal rise and run, but negative). Using \(y=mx + b\) with \(m=-1\) and \(b = 0\), the equation is \(y=-x\), which corresponds to option A.

Final Answers:

• Graph 1: F. \(y = x\)
• Graph 2: E. \(y = x + 4\)
• Graph 3: A. \(y=-x\)