Consider the equation 4x + 6y = 48.

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 IN PERFECT GRAMMER
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)

"Perfect Grammar"? (SIC)

Pray tell, I know what correct and incorrect grammar is , but "perfect" grammar is unknown to me.

We will be happy to critique your writing. (and math thinking, which is supposed to be the point, I would hope)

Part 1: Slope-Intercept Method

To graph the equation 4x + 6y = 48 using the slope-intercept method, I followed these steps:

Step 1: Write the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
In this case, the given equation is 4x + 6y = 48.
To isolate the y-term, I subtracted 4x from both sides and got 6y = -4x + 48.

Step 2: Divide both sides of the equation by 6 to solve for y.
By dividing by 6, I obtained y = (-4/6)x + 8, which simplifies to y = (-2/3)x + 8.

Step 3: Now I have the equation in slope-intercept form (y = mx + b), where the slope is -2/3 and the y-intercept is 8.
The slope is -2/3, which means that for every 3 units I move to the right on the x-axis, I need to move 2 units downward on the y-axis.
The y-intercept is 8, which represents the point (0, 8) on the graph.

Step 4: Starting from the y-intercept (0, 8), I used the slope (-2/3) to locate additional points.
I moved 3 units to the right from (0, 8) on the x-axis and then 2 units downward on the y-axis, which gave me the point (3, 6).
I repeated this process to locate more points, such as (6, 4) and (9, 2).

Step 5: I connected all the points I found on the graph to draw a straight line.
The line represents all the possible solutions (x, y) that satisfy the equation 4x + 6y = 48.

Part 2: Intercepts Method

To graph the equation 4x + 6y = 48 using the intercepts method, I followed these steps:

Step 1: To find the x-intercept, I set y equal to 0 and solved for x.
By substituting y = 0 into the equation, I got 4x + 6(0) = 48.
Simplifying further, I obtained 4x = 48, and by dividing both sides by 4, I found x = 12.
Therefore, the x-intercept is (12, 0).

Step 2: To find the y-intercept, I set x equal to 0 and solved for y.
By substituting x = 0 into the equation, I got 4(0) + 6y = 48.
Simplifying further, I obtained 6y = 48, and by dividing both sides by 6, I found y = 8.
Therefore, the y-intercept is (0, 8).

Step 3: I plotted the x-intercept (12, 0) and the y-intercept (0, 8) on the graph.

Step 4: Since I already have two points, the x-intercept and the y-intercept, I connected them with a straight line.
The line represents all the possible solutions (x, y) that satisfy the equation 4x + 6y = 48.

Part 1: To graph the equation 4x + 6y = 48 using the slope-intercept method, we need to rewrite the equation in the form y = mx + b, where m is the slope and b is the y-intercept.

Step 1: Start by isolating the y variable. Subtract 4x from both sides of the equation to get:
6y = -4x + 48.

Step 2: Divide both sides of the equation by 6 to solve for y:
y = (-4/6)x + 8.

Step 3: Now we can easily identify the slope and y-intercept. The slope is -4/6, which simplifies to -2/3. The y-intercept is 8.

Step 4: Plot the y-intercept on the graph. This means marking the point (0, 8), where the line crosses the y-axis.

Step 5: Use the slope to find additional points. With a slope of -2/3, we can move down 2 units and to the right 3 units from the y-intercept point. Mark another point at (-3, 6).

Step 6: Connect the two points on the graph with a straight line.

Part 2: To graph the equation 4x + 6y = 48 using the intercepts method:

Step 1: To find the x-intercept, set y = 0 and solve for x.
4x + 6(0) = 48.
4x = 48.
Divide both sides by 4 to get:
x = 12.
So the x-intercept is (12, 0).

Step 2: To find the y-intercept, set x = 0 and solve for y.
4(0) + 6y = 48.
6y = 48.
Divide both sides by 6 to get:
y = 8.
So the y-intercept is (0, 8).

Step 3: Plot the x-intercept (12, 0) and the y-intercept (0, 8) on the graph.

Step 4: Draw a straight line through these two points to represent the equation 4x + 6y = 48.