Question

1. a. x: 1, 2, 3, 4; y: -2, 0, 2, 4 (with a coordinate grid below the table)

Explanation:

Step1: Identify Coordinates

From the table, the points are \((1, -2)\), \((2, 0)\), \((3, 2)\), \((4, 4)\).

Step2: Plot Points on Graph

• For \(x = 1\), \(y=-2\): Locate \(x = 1\) on the x - axis and \(y=-2\) on the y - axis, mark the point.
• For \(x = 2\), \(y = 0\): Locate \(x = 2\) on the x - axis and \(y = 0\) (on the x - axis), mark the point.
• For \(x = 3\), \(y = 2\): Locate \(x = 3\) on the x - axis and \(y = 2\) on the y - axis, mark the point.
• For \(x = 4\), \(y = 4\): Locate \(x = 4\) on the x - axis and \(y = 4\) on the y - axis, mark the point.

(Note: Since the problem seems to be about plotting the points from the table on the given coordinate plane, the final action is to plot these points. If we were to find the equation, we can also do that. Let's find the slope between two points, say \((1,-2)\) and \((2,0)\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0-(-2)}{2 - 1}=\frac{2}{1}=2\). Using point - slope form \(y - y_1=m(x - x_1)\) with \((1,-2)\), we get \(y+2 = 2(x - 1)\), which simplifies to \(y=2x-4\). We can check for other points: when \(x = 3\), \(y=2(3)-4 = 2\) (matches), when \(x = 4\), \(y=2(4)-4 = 4\) (matches).)

Answer:

The points \((1, -2)\), \((2, 0)\), \((3, 2)\), \((4, 4)\) are plotted on the coordinate plane. The equation of the line passing through these points is \(y = 2x-4\).