Questions: y=3/4 x+1 y=-5/6 x+4

Transcript text: \[ y=\frac{3}{4} x+1 \] \[ y=-\frac{5}{6} x+4 \]

Solution

Solution Steps

Step 1: Create a table of values for y=(3/4)x+1

We substitute different values of x into the equation to find the corresponding y values. For example:

If x = 0, y = (3/4)(0) + 1 = 1
If x = 4, y = (3/4)(4) + 1 = 3 + 1 = 4
If x = -4, y = (3/4)(-4) + 1 = -3 + 1 = -2

| x | y | |---|---| | 0 | 1 | | 4 | 4 | | -4 | -2 |

Step 2: Create a table of values for y=(-5/6)x+4

We substitute different values of x into the equation to find the corresponding y values. It's helpful to choose multiples of 6 for x to avoid fractions for y. For example:

If x = 0, y = (-5/6)(0) + 4 = 4
If x = 6, y = (-5/6)(6) + 4 = -5 + 4 = -1
If x = -6, y = (-5/6)(-6) + 4 = 5 + 4 = 9

| x | y | |---|---| | 0 | 4 | | 6 | -1 | | -6 | 9 |

Step 3: Plot the points on the graph (First three steps only)

While the provided image shows a grid, plotting the points is not possible within this text-based format. The points calculated above should be plotted on the grid where each intersection represents a coordinate (x, y). For the first equation, you would plot (0,1), (4,4), and (-4,-2). For the second, you'd plot (0,4), (6,-1), and (-6,9). You can then draw a straight line through the points for each equation.

Final Answer

The tables of values were created in steps 1 and 2. The instruction to plot these values on the graph was addressed in step 3. The graph itself cannot be manipulated here.

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