Question

1. graph each relation for integer values of x from 0 to 5. a) $y = 2x$ b) $y = 3x$ c) $y = 4x$ d) $y = 5x$ e) $y = -2x$ f) $y = -3x$ g) $y = -4x$ h) $y = -5x$

Explanation:

Part (a): \( y = 2x \)

Step 1: Find \( y \) for \( x = 0 \) to \( 5 \)

For \( x = 0 \): \( y = 2(0) = 0 \)
For \( x = 1 \): \( y = 2(1) = 2 \)
For \( x = 2 \): \( y = 2(2) = 4 \)
For \( x = 3 \): \( y = 2(3) = 6 \)
For \( x = 4 \): \( y = 2(4) = 8 \)
For \( x = 5 \): \( y = 2(5) = 10 \)

Step 2: Plot the points \((0,0)\), \((1,2)\), \((2,4)\), \((3,6)\), \((4,8)\), \((5,10)\) and draw a line through them.

Part (b): \( y = 3x \)

Step 1: Find \( y \) for \( x = 0 \) to \( 5 \)

For \( x = 0 \): \( y = 3(0) = 0 \)
For \( x = 1 \): \( y = 3(1) = 3 \)
For \( x = 2 \): \( y = 3(2) = 6 \)
For \( x = 3 \): \( y = 3(3) = 9 \)
For \( x = 4 \): \( y = 3(4) = 12 \)
For \( x = 5 \): \( y = 3(5) = 15 \)

Step 2: Plot the points \((0,0)\), \((1,3)\), \((2,6)\), \((3,9)\), \((4,12)\), \((5,15)\) and draw a line through them.

Part (c): \( y = 4x \)

Step 1: Find \( y \) for \( x = 0 \) to \( 5 \)

For \( x = 0 \): \( y = 4(0) = 0 \)
For \( x = 1 \): \( y = 4(1) = 4 \)
For \( x = 2 \): \( y = 4(2) = 8 \)
For \( x = 3 \): \( y = 4(3) = 12 \)
For \( x = 4 \): \( y = 4(4) = 16 \)
For \( x = 5 \): \( y = 4(5) = 20 \)

Step 2: Plot the points \((0,0)\), \((1,4)\), \((2,8)\), \((3,12)\), \((4,16)\), \((5,20)\) and draw a line through them.

Part (d): \( y = 5x \)

Answer:

(Summary of Steps for Each Part):
For each relation \( y = kx \) (or \( y = -kx \)):

1. Calculate \( y \) for \( x = 0, 1, 2, 3, 4, 5 \) using the equation.
2. Plot the ordered pairs \((x, y)\) on a coordinate plane.
3. Draw a straight line through the plotted points.

(Note: Graphs will show linear relationships—positive slopes for \( y = kx \), negative slopes for \( y = -kx \), all passing through the origin.)