Final answer:
To graph the equation 7x + 6y = 18, rearrange it in terms of y by subtracting 7x from both sides and dividing by 6. The resulting equation is y = (-7/6)x + 3. Plot the y-intercept at (0, 3) and find other points on the line by substituting different values of x into the equation.
Step-by-step explanation:
Solving 7x + 6y = 18 on a graph:
To graph the equation 7x + 6y = 18, we need to rearrange it in terms of y. Start by subtracting 7x from both sides to isolate the y term. This gives us 6y = -7x + 18. Next, divide both sides by 6 to solve for y, resulting in y = (-7/6)x + 3.
In this equation, the coefficient of x, which is -7/6, represents the slope of the line. The y-intercept is 3, which is the point where the line crosses the y-axis.
To graph this line, plot the y-intercept at (0, 3), and then find a few other points on the line by substituting different values of x into the equation and calculating the corresponding y values. Connect these points to form the line. The graph should be a straight line with a negative slope.