Question

Write the equation in slope-intercept form. Then graph the equation. $$ x+3 y-3=0 $$

Short answer

The equation in slope-intercept form is \(y = -(1/3)x + 1\). The slope is \(-1/3\) and the y-intercept is 1. A graph of the equation shows a slope of \(-1/3\) starting from the point (0,1).

Step-by-step solution

Rewrite Equation in slope-intercept form

The first step will be rearranging the given equation, \(x + 3y - 3 = 0\), into the slope-intercept form. This could be done by isolating \(y\) on one side of the equation. So the equation becomes \(3y = -x + 3 \). Finally, divide through by 3 to isolate \(y\), obtaining \(y = -(1/3)x + 1\).

Define Slope and y-intercept

From the equation obtained in step 1, we can therefore determine that the slope \(m\) of the line is \(-1/3\) and the y-intercept \(b\) is 1.

Graph the Equation

To graph the equation, plot the y-intercept first, which is the point (0, 1). Starting from this point, use the slope to find additional points. The slope \(-1/3\) means for every 1 unit decrease in \(x\), \(y\) increases by 3. Alternatively, for every 3 units increase in \(x\), \(y\) decreases by 1. Draw a line through these points to complete the graph.