To graph the line [tex]\( y=5(x-1)-2 \)[/tex] using the given table of values, we will follow these steps:
1. Identify Points from the Table: We need to select at least two points from the provided table of values to plot on the graph.
Here are some points from the given table:
- [tex]\((-10, -57)\)[/tex]
- [tex]\((-9, -52)\)[/tex]
- [tex]\((-8, -47)\)[/tex]
- [tex]\((-7, -42)\)[/tex]
- [tex]\((-6, -37)\)[/tex]
- [tex]\((-5, -32)\)[/tex]
- [tex]\((-4, -27)\)[/tex]
- [tex]\((-3, -22)\)[/tex]
- [tex]\((-2, -17)\)[/tex]
- [tex]\((-1, -12)\)[/tex]
- [tex]\((0, -7)\)[/tex]
- [tex]\((1, -2)\)[/tex]
- [tex]\((2, 3)\)[/tex]
- [tex]\((3, 8)\)[/tex]
- [tex]\((4, 13)\)[/tex]
- [tex]\((5, 18)\)[/tex]
- [tex]\((6, 23)\)[/tex]
- [tex]\((7, 28)\)[/tex]
- [tex]\((8, 33)\)[/tex]
- [tex]\((9, 38)\)[/tex]
- [tex]\((10, 43)\)[/tex]
2. Select Points to Plot: We can select two points from the table for plotting. Let's choose the points [tex]\((-10, -57)\)[/tex] and [tex]\((-9, -52)\)[/tex].
3. Plot the Points:
- Plot the point at [tex]\((-10, -57)\)[/tex].
- Plot the point at [tex]\((-9, -52)\)[/tex].
4. Draw the Line: Using these two points, we can draw a straight line through the points. This line represents the graph of the equation [tex]\( y = 5(x-1) - 2 \)[/tex].
Given plot points [tex]\((-10, -57)\)[/tex] and [tex]\((-9, -52)\)[/tex] we can also notice from these values that as [tex]\( x \)[/tex] increases by 1, [tex]\( y \)[/tex] increases by [tex]\( 5 \)[/tex]. This verifies the linear relationship defined by the equation [tex]\( y = 5(x - 1) - 2 \)[/tex].
