Question

4 multiple choice 10 points which best represents the equation of the line graphed? graph of a line on a coordinate plane options: y = 2x - 3; y = 2x; y = (1/2)x - 3; y = -2x - 3

Explanation:

Step1: Identify the slope-intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

Step2: Find the y - intercept (\(b\))

The y - intercept is the point where the line crosses the y - axis. From the graph, the line crosses the y - axis at \((0,-3)\), so \(b=-3\).

Step3: Calculate the slope (\(m\))

We can use two points on the line. Let's take the y - intercept \((0, - 3)\) and another point, for example, \((1,-1)\) (we can also use \((2,1)\) or other points). The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \((x_1,y_1)=(0,-3)\) and \((x_2,y_2)=(1,-1)\), we have \(m=\frac{-1-(-3)}{1 - 0}=\frac{-1 + 3}{1}=\frac{2}{1}=2\).

Step4: Determine the equation

Since \(m = 2\) and \(b=-3\), the equation of the line in slope - intercept form is \(y=2x-3\).

Answer:

\(y = 2x-3\) (the first option: \(y = 2x-3\))