Question

1. make a table and graph the equation with 3 ordered pairs

5y = -2x + 5

1. graph the equation x = -3.
2. graph the equation y = 4.

Explanation:

Problem 33:

Step1: Solve for y

First, we solve the equation \(5y = -2x + 5\) for \(y\) by dividing each term by 5:
\(y=\frac{-2x + 5}{5}=-\frac{2}{5}x + 1\)

Step2: Choose x-values

We can choose three convenient \(x\)-values, say \(x = 0\), \(x = 5\), and \(x=-5\) (to eliminate the fraction).

Step3: Calculate y for x=0

Substitute \(x = 0\) into \(y=-\frac{2}{5}x + 1\):
\(y=-\frac{2}{5}(0)+1 = 1\)

Step4: Calculate y for x=5

Substitute \(x = 5\) into \(y=-\frac{2}{5}x + 1\):
\(y=-\frac{2}{5}(5)+1=-2 + 1=-1\)

Step5: Calculate y for x=-5

Substitute \(x=-5\) into \(y=-\frac{2}{5}x + 1\):
\(y=-\frac{2}{5}(-5)+1 = 2 + 1=3\)

The table of ordered pairs is:

\(x\)	\(y\)
\(5\)	\(-1\)
\(-5\)	\(3\)

To graph: Plot the points \((0, 1)\), \((5, -1)\), and \((-5, 3)\) on the coordinate plane and draw a straight line through them.

Problem 34:

The equation \(x=-3\) represents a vertical line. A vertical line has the same \(x\)-value (\(-3\)) for all \(y\)-values.

To graph: Locate \(x=-3\) on the \(x\)-axis (3 units to the left of the origin). Draw a straight vertical line through this point, parallel to the \(y\)-axis. This line will pass through all points where \(x=-3\) (e.g., \((-3, 0)\), \((-3, 2)\), \((-3, -4)\), etc.).

Problem 35:

The equation \(y = 4\) represents a horizontal line. A horizontal line has the same \(y\)-value (\(4\)) for all \(x\)-values.

To graph: Locate \(y = 4\) on the \(y\)-axis (4 units above the origin). Draw a straight horizontal line through this point, parallel to the \(x\)-axis. This line will pass through all points where \(y = 4\) (e.g., \((0, 4)\), \((2, 4)\), \((-3, 4)\), etc.).

Answer:

s:

1. Table:

\(x\)	\(y\)
\(5\)	\(-1\)
\(-5\)	\(3\)

Graph: Line through \((0, 1)\), \((5, -1)\), \((-5, 3)\).

1. Graph: Vertical line through \(x=-3\).

1. Graph: Horizontal line through \(y = 4\).