Question

Find the slope and the \(y\) -intercept of the graph of the equation. Then graph the equation. $$ y+2 x=2 $$

Short answer

The slope of the equation \(y + 2x = 2\) is -2, and the y-intercept is 2. The graph of the line starts at point (0,2) on the y-axis. From there, the line moves down 2 units and right 1 unit for each step due to the slope of -2/1.

Step-by-step solution

Arrange Equation to Slope-Intercept Form

First, arrange the given equation \(y + 2x = 2\) in the form of \(y = mx + b\). For this, subtract \(2x\) from both sides to isolate \(y\). This would result in \(y = -2x + 2\).

Identify the Slope and Y-intercept

With the equation \(y = -2x + 2\), it is clear that \(m=-2\), which is the slope of the equation, and \(b=2\), which is the y-intercept.

Plotting the Equation

To plot the graph for the equation, firstly mark the y-intercept point at \(y = 2\) on the y-axis. Then, use the slope to determine the next point. Since the slope is -2, which can also be written as -2/1, start at the y-intercept and move 2 units downward (negative sign indicates downward movement) and 1 unit in the positive x direction (denominator indicates rightward movement). Repeat this process several times to establish a series of points, then connect the points to form a straight line.