Find the x-intercept by solving a given equation, for example: 3x + 5y - 30 = 0, when y = 0. Substitute 0 for y and isolate x by adding -30 to both sides: 3x + 5(0) - 30 + 30 = 30, resulting in 3x = 30. Multiply both sides by 1/3 to get the value of x: 3x (1/3 ) = 30 (1/3), or x = 10. The x-intercept is the point (10, 0).
Find the y-intercept by setting the value of x equal to 0 and isolating y: 3(0) + 5y - 30 + 30 = 30, resulting in 5y = 30. Multiply (1/5) to both sides to get the value of the y-intercept: 5y(1/5) = 30 (1/5), or y = 6. The y-intercept is the point (0, 6).
Draw the x and y axes on a sheet of graph paper and number them through 15. Plot the x and y-intercepts: (10, 0) and (0, 6) and draw the line connecting these points, which is the graph for the equation: 3x + 5y - 30 = 0.