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.
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.
sorry - no paper here
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 and correct grammar.
Part 1: Slope-Intercept Method
To graph the equation 4x + 6y = 48 using the slope-intercept method:
Step 1: Start by solving the equation for y to get it in slope-intercept form (y = mx + b). In this case, we want to isolate y, so we subtract 4x from both sides of the equation:
6y = -4x + 48.
Step 2: Divide the entire equation by 6 to solve for y:
y = -4/6x + 8.
Step 3: From the equation, we can observe that the coefficient of x (-4/6) is the slope (m), and the constant term (8) is the y-intercept (b).
Step 4: Start by plotting the y-intercept, which is the point (0, 8). This is the point where the graph intersects the y-axis.
Step 5: Next, determine the slope, which in this case is -4/6. The slope indicates how the graph will slant. Since the slope is negative, the line will slope downwards from left to right.
Step 6: Use the slope to find additional points to plot on the graph. To do this, start from the y-intercept and count down 4 units vertically and then count to the right 6 units horizontally. This gives you another point on the line.
Step 7: Repeat step 6 to find a third point on the graph.
Step 8: Once you have at least two points, draw a straight line through them to complete the graph.
Part 2: Intercepts Method
To graph the equation 4x + 6y = 48 using the intercepts method:
Step 1: The x-intercept is the point where the graph intersects the x-axis. To find it, set y = 0 in the equation and solve for x.
4x + 6(0) = 48,
4x = 48,
x = 48/4,
x = 12.
So the x-intercept is (12, 0).
Step 2: The y-intercept is the point where the graph intersects the y-axis. To find it, set x = 0 in the equation and solve for y.
4(0) + 6y = 48,
6y = 48,
y = 48/6,
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 the two points to complete the graph.
By following these steps, you can graph the equation 4x + 6y = 48 using both the slope-intercept method and the intercepts method.