Question

write the equation of the line in fully simplified slope-intercept form.

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through the points \((0, -3)\) (the y - intercept) and \((2, 0)\). We can also use other points like \((4, 3)\), \((6, 6)\), \((8, 9)\) etc. Let's use \((0, -3)\) and \((2, 0)\).

Step2: Calculate the slope (\(m\))

The formula for slope between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Using \((x_1,y_1)=(0, - 3)\) and \((x_2,y_2)=(2,0)\), we have \(m=\frac{0-(-3)}{2 - 0}=\frac{0 + 3}{2}=\frac{3}{2}\).

Step3: Determine the y - intercept (\(b\))

The slope - intercept form of a line is \(y=mx + b\), where \(b\) is the y - intercept (the value of \(y\) when \(x = 0\)). From the point \((0,-3)\), when \(x = 0\), \(y=-3\), so \(b=-3\).

Step4: Write the equation

Substitute \(m=\frac{3}{2}\) and \(b = - 3\) into the slope - intercept form \(y=mx + b\).
We get \(y=\frac{3}{2}x-3\).

Answer:

\(y=\frac{3}{2}x - 3\)