Final answer:
To graph the equation 6x+2y=10, calculate the x- and y-intercepts which are (5/3, 0) and (0, 5) respectively. Plot these points on a labeled graph with the scales adjusted for the maximum values, and then draw a line through the points to represent the equation.
Step-by-step explanation:
To graph the equation 6x+2y=10, we need two points. Let's find the intercepts. For the x-intercept, set y to 0 and solve for x:
6x + 2(0) = 10 → 6x = 10 → x = 10/6 → x = 5/3.
Now, let's find the y-intercept by setting x to 0:
6(0) + 2y = 10 → 2y = 10 → y = 5.
Plot the points (5/3, 0) and (0, 5) on the graph and draw a straight line through them. This line represents the equation 6x+2y=10. Ensure to label the graph with f(x) and x, and scale the axes according to the maximum values. If f(x) = 10, and 0≤x≤ 20, the x-axis should go up to 20 and include negative values as needed, while the y-axis should be scaled to include at least the value of 5.
Remember, you can check your work by choosing another value for x or y, solving for the other variable, and ensuring that this point also lies on the line you have drawn.