Consider the equation 5x + 2y = 30.

Part 1: On your own paper, graph this equation using the slope-intercept method. In the space provided, explain, in words, each step of the procedure you used. Make sure to use complete sentences and correct grammar. (3 points)
Part 2: On your own paper, graph this equation using the intercepts method. In the space provided, explain, in words, each step of the procedure you used. Make sure to use complete sentences and correct grammar. (3 points)

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Part 1: To graph the equation 5x + 2y = 30 using the slope-intercept method, follow these steps:

1. Begin by isolating y on one side of the equation. Subtract 5x from both sides to get 2y = -5x + 30.
2. Divide both sides of the equation by 2 to find the coefficient of y. This gives us y = (-5/2)x + 15.
3. Now we have the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope (m) is -5/2 and the y-intercept (b) is 15.
4. To plot the graph, start by locating the y-intercept on the y-axis. Mark a point at (0, 15).
5. Once you have the y-intercept, use the slope to find additional points. The slope (-5/2) tells us that for every 2 units we move to the right, we need to move down 5 units. So, starting from the y-intercept, move 2 units to the right and 5 units down to find another point.
6. Repeat step 5 to find more points if needed.
7. Finally, connect the points with a straight line to graph the equation.

Part 2: To graph the equation 5x + 2y = 30 using the intercepts method, follow these steps:

1. To find the x-intercept, set y = 0 in the equation and solve for x. Substituting y = 0 into the equation gives us 5x + 2(0) = 30. Simplifying further, we get 5x = 30, which gives us x = 6.
2. So, the x-intercept is at (6, 0). Mark this point on the graph.
3. To find the y-intercept, set x = 0 in the equation and solve for y. Substituting x = 0 into the equation gives us 5(0) + 2y = 30. Simplifying further, we get 2y = 30, which gives us y = 15.
4. Therefore, the y-intercept is at (0, 15). Mark this point on the graph.
5. Now we have the x-intercept and the y-intercept. Plot these two points on the graph.
6. Finally, connect the two intercept points with a straight line to graph the equation.