Consider the equation 7x + 3y = 42.

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)

Your equation is perfect for finding intercepts.

let x=0 , (put your little finger over the 7x term), then y = 14
let y = 0, ( put your little finger over the 3y term), then x = 6
so you have 2 nice points, (0,14) and (6,0)

to change to slope-yintercept form
3y = -7x + 42
y = (-7/3)x + 14

I am not certain of your question about this. I will be happy to critique your thinking.

I just need to show the work from getting the equation 7x + 3y = 42 into slope- intercept form. Then I need the step by step work for graphing it in intercepts form.

Thank you!

1. 7X + 3Y = 42.

Convert the std form Eq to the slope-interceptform:
7X + 3Y = 42,
3Y = -7X + 42,
Y = -7/3X + 14, (Y = mx + b).
Our 1st point will be at the Y-int
where X is always 0.
P1(0 , 14).

Since our slope is neg. DECREASE
b by 7:
y = 14 - 7 = 7.
X = 3 = The denominator of the slope.
P2(3 , 7).

GRAPH: P1(0 , 14) , P2(3 , 7)

2. 7X + 3Y = 42
At the y-int., X = 0.
Calculate Y:
7(0) + 3Y = 42
3Y = 42
Y = 14.
P1(0 , 14).

At the X-INT, Y = 0.
Calculate X:
7X + 3(0) = 42,
7X = 42,
X = 6.
P2(6 , 0).

GRAPH: P1(0 , 14) , P2(6 , 0).

Part 1: Graphing using the slope-intercept method

Step 1: Start by rearranging the given equation into the slope-intercept form, y = mx + b. In this case, we have 7x + 3y = 42. To do this, isolate the y variable by subtracting 7x from both sides: 3y = -7x + 42.

Step 2: Divide both sides of the equation by 3 to solve for y: y = (-7/3)x + 14.

Step 3: Now, we can identify the slope (m) and the y-intercept (b) of the equation. The coefficient of x (-7/3) represents the slope, while the constant term (14) represents the y-intercept.

Step 4: To graph the equation, plot the y-intercept first. In this case, the y-intercept is at the point (0, 14), which means when x = 0, y = 14.

Step 5: Next, use the slope-value (-7/3) to determine the direction of the line. Since the slope is negative and in fraction form, we can interpret it as "going down 7 units vertically and 3 units to the right." Starting from the y-intercept point, move down 7 units and then to the right 3 units. Plot this new point.

Step 6: Repeat Step 5 until you have enough points to draw a line. Connect the plotted points with a straight line. The line represents all the possible solutions to the equation 7x + 3y = 42.

Part 2: Graphing using the intercepts method

Step 1: To graph using the intercepts method, we find the x-intercept and the y-intercept of the equation.

Step 2: To find the x-intercept, set y = 0 in the equation and solve for x. So, substitute y with 0 in 7x + 3y = 42: 7x + 3(0) = 42. Simplify the equation to find the x-intercept: 7x = 42. Divide both sides by 7, x = 6. The x-intercept is at (6, 0), meaning when y = 0, x = 6.

Step 3: To find the y-intercept, set x = 0 in the equation and solve for y. Similarly, substitute x with 0 in 7x + 3y = 42: 7(0) + 3y = 42. Simplify the equation to find the y-intercept: 3y = 42. Divide both sides by 3, y = 14. The y-intercept is at (0, 14), meaning when x = 0, y = 14.

Step 4: Plot the x-intercept (6, 0) and the y-intercept (0, 14) on the coordinate plane.

Step 5: With the two intercept points, draw a straight line passing through both points. This line represents all the possible solutions to the equation 7x + 3y = 42.

By following these steps, you should be able to graph the equation 7x + 3y = 42 using both the slope-intercept method and the intercepts method on your own paper.