The equation in slope-intercept form is y=− 1/6x+1.
To convert the equation 3x+18y=18 into slope-intercept form (y=mx+b), where m is the slope and b is the y-intercept, we can manipulate the equation to isolate y. First, subtract 3x from both sides of the equation:
18y=−3x+18
Next, divide both sides by 18 to solve for y:
y=− 1/6x+1
Now, the equation is in slope-intercept form. The slope (m) is −1/6, and the y-intercept (b) is 1. This means that for every increase of 1 unit in the x-direction, the y-value decreases by 1/6.
To graph the equation on the coordinate plane, plot the y-intercept at (0,1), and use the slope to find additional points. For example, move one unit to the right and three units down to get another point on the line. Connect the points to draw the line.