Question

find the equation of this line.
simplify your answer completely.
y = ?x + \square

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through the points \((0, -4)\) (the y - intercept) and \((2, 2)\).

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

The formula for the slope between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting \(x_1 = 0,y_1=-4,x_2 = 2,y_2 = 2\) into the formula:
\(m=\frac{2-(-4)}{2 - 0}=\frac{2 + 4}{2}=\frac{6}{2}=3\)

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

The y - intercept is the value of \(y\) when \(x = 0\). From the point \((0,-4)\), we can see that \(b=-4\).

Step4: Write the equation of the line

The slope - intercept form of a line is \(y=mx + b\). Substituting \(m = 3\) and \(b=-4\) into the formula, we get \(y = 3x-4\).

Answer:

The equation of the line is \(y=\boldsymbol{3}x+\boldsymbol{(-4)}\) (or \(y = 3x-4\))