To graph the equation [tex]\(-8 + x = 4y - 16\)[/tex], let's go through the steps to reorganize and find two points on the line.
1. Rewrite the equation:
[tex]\[-8 + x = 4y - 16\][/tex]
2. Isolate [tex]\(y\)[/tex]:
Add 16 to both sides to start:
[tex]\[x + 8 = 4y\][/tex]
Now, divide both sides by 4 to solve for [tex]\(y\)[/tex]:
[tex]\[y = \frac{x + 8}{4}\][/tex]
Now we have the equation of the line in slope-intercept form [tex]\(y = \frac{1}{4}x + 2\)[/tex].
3. Find two points:
- Point 1 (when [tex]\(x = 0\)[/tex]):
[tex]\[y = \frac{0 + 8}{4} = \frac{8}{4} = 2\][/tex]
So, the first point is [tex]\((0, 2)\)[/tex].
- Point 2 (when [tex]\(x = 4\)[/tex]):
[tex]\[y = \frac{4 + 8}{4} = \frac{12}{4} = 3\][/tex]
So, the second point is [tex]\((4, 3)\)[/tex].
4. Graphing the line:
- Plot the first point [tex]\((0, 2)\)[/tex] on the graph.
- Plot the second point [tex]\((4, 3)\)[/tex] on the graph.
- Draw a straight line through these two points, extending in both directions.
Using these two points, [tex]\((0, 2)\)[/tex] and [tex]\((4, 3)\)[/tex], correctly graphs the equation [tex]\(-8 + x = 4y - 16\)[/tex].
