Question

write each equation in slope - intercept form (y=mx + b). then sketch the graph of each line.

1. 3x - 4y = 12
2. 4x + 5y=-5
3. 3x + 4y=-8
4. 2x - y=-4

write the slope - intercept form of the equation of each line. solve for y (y=mx + b)

1. x - 4y = 8
2. 10x - 7y = 35
3. 2x + y = 2
4. 8x + y = 1

Explanation:

1. For the equation \(3x - 4y=12\):

• Explanation:
• Step 1: Isolate the \(y\) - term

Subtract \(3x\) from both sides of the equation: \(-4y=-3x + 12\).

• Step 2: Solve for \(y\)

Divide each term by \(-4\): \(y=\frac{3}{4}x-3\).

1. For the equation \(4x + 5y=-5\):

• Explanation:
• Step 1: Isolate the \(y\) - term

Subtract \(4x\) from both sides: \(5y=-4x - 5\).

• Step 2: Solve for \(y\)

Divide each term by \(5\): \(y =-\frac{4}{5}x-1\).

1. For the equation \(3x + 4y=-8\):

• Explanation:
• Step 1: Isolate the \(y\) - term

Subtract \(3x\) from both sides: \(4y=-3x - 8\).

• Step 2: Solve for \(y\)

Divide each term by \(4\): \(y=-\frac{3}{4}x - 2\).

1. For the equation \(2x-y=-4\):

• Explanation:
• Step 1: Isolate the \(y\) - term

Subtract \(2x\) from both sides: \(-y=-2x - 4\).

• Step 2: Solve for \(y\)

Multiply both sides by \(- 1\): \(y = 2x+4\).

1. For the equation \(x - 4y=8\):

• Explanation:
• Step 1: Isolate the \(y\) - term

Subtract \(x\) from both sides: \(-4y=-x + 8\).

• Step 2: Solve for \(y\)

Divide each term by \(-4\): \(y=\frac{1}{4}x - 2\).

1. For the equation \(10x-7y = 35\):

• Explanation:
• Step 1: Isolate the \(y\) - term

Subtract \(10x\) from both sides: \(-7y=-10x + 35\).

• Step 2: Solve for \(y\)

Divide each term by \(-7\): \(y=\frac{10}{7}x - 5\).

1. For the equation \(2x + y=2\):

• Explanation:
• Step 1: Isolate the \(y\) - term

Subtract \(2x\) from both sides: \(y=-2x + 2\).

1. For the equation \(8x + y=1\):

• Explanation:
• Step 1: Isolate the \(y\) - term

Subtract \(8x\) from both sides: \(y=-8x + 1\).

To sketch the graphs:

• For \(y = mx + b\), the \(y\) - intercept is the point \((0,b)\), and the slope \(m\) gives the rate of change. For example, if \(m=\frac{a}{b}\), from a given point on the line, you move \(a\) units up (if \(a>0\)) or down (if \(a < 0\)) and \(b\) units to the right to find another point on the line.

• For \(y=\frac{3}{4}x-3\), the \(y\) - intercept is \((0, - 3)\) and the slope is \(\frac{3}{4}\).
• For \(y=-\frac{4}{5}x-1\), the \(y\) - intercept is \((0,-1)\) and the slope is \(-\frac{4}{5}\).
• For \(y=-\frac{3}{4}x - 2\), the \(y\) - intercept is \((0,-2)\) and the slope is \(-\frac{3}{4}\).
• For \(y = 2x+4\), the \(y\) - intercept is \((0,4)\) and the slope is \(2\).
• For \(y=\frac{1}{4}x - 2\), the \(y\) - intercept is \((0,-2)\) and the slope is \(\frac{1}{4}\).
• For \(y=\frac{10}{7}x - 5\), the \(y\) - intercept is \((0,-5)\) and the slope is \(\frac{10}{7}\).
• For \(y=-2x + 2\), the \(y\) - intercept is \((0,2)\) and the slope is \(-2\).
• For \(y=-8x + 1\), the \(y\) - intercept is \((0,1)\) and the slope is \(-8\).

Answer:

• \(y=\frac{3}{4}x-3\)
• \(y=-\frac{4}{5}x-1\)
• \(y=-\frac{3}{4}x - 2\)
• \(y = 2x+4\)
• \(y=\frac{1}{4}x - 2\)
• \(y=\frac{10}{7}x - 5\)
• \(y=-2x + 2\)
• \(y=-8x + 1\)