Question

Write the equation in slope-intercept form. Then graph the equation. $$ x+2 y-6=0 $$

Short answer

The equation in slope-intercept form is \(y = -0.5x + 3\). The graph of this equation starts at the point (0,3) and slopes downward at a gradient of -0.5.

Step-by-step solution

Convert to Slope-Intercept Form

The equation can be converted into the slope-intercept form by rearranging the equation: \(x+2y-6=0\) to \(2y = -x + 6\), and then divide by 2 to find \(y\), giving \(y = -0.5x + 3\).

Identify the Slope and Y-intercept

From the equation \(y = -0.5x + 3\), it can be observed that the slope 'm' is -0.5 and the y-intercept 'b' is 3.

Graph the Equation

Begin by plotting the y-intercept (0,3). From here, take the slope (-0.5) which means when 'x' increases by 1, 'y' decreases by 0.5. Continue this process until you have enough points to make a graph. Sketch the line that runs through these points.