Question

1. which equation correctly represents the line graphed below? 1 point

Explanation:

To determine the equation of the line, we use the slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

Step 1: Find the y - intercept (\(b\))

The y - intercept is the value of \(y\) when \(x = 0\). From the graph, we can see that the line crosses the y - axis at \((0,12)\). So, \(b=12\).

Step 2: Calculate the slope (\(m\))

The slope \(m\) is calculated using the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). We can pick two points on the line. Let's use the points \((0,12)\) and \((3,18)\) (we can also use other pairs of points from the line).
Substitute \(x_1 = 0,y_1 = 12,x_2=3,y_2 = 18\) into the slope formula:
\(m=\frac{18 - 12}{3-0}=\frac{6}{3}=2\)

Step 3: Write the equation of the line

Now that we know \(m = 2\) and \(b = 12\), substitute these values into the slope - intercept form \(y=mx + b\).
We get \(y=2x + 12\)

Answer:

The equation of the line is \(y = 2x+12\)