To graph the equation [tex]\( -4y = -5x - 18 \)[/tex] by plotting three points, follow these steps:
1. Rewrite the equation to express [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex]:
Start with the original equation:
[tex]\( -4y = -5x - 18 \)[/tex]
Divide both sides by [tex]\(-4\)[/tex] to isolate [tex]\( y \)[/tex]:
[tex]\[
y = \frac{-5x - 18}{-4}
\][/tex]
Simplify the equation:
[tex]\[
y = \frac{5x + 18}{4}
\][/tex]
2. Choose three values for [tex]\( x \)[/tex]:
Let's select [tex]\( x = -1 \)[/tex], [tex]\( x = 0 \)[/tex], and [tex]\( x = 1 \)[/tex].
3. Calculate the corresponding [tex]\( y \)[/tex]-values:
For [tex]\( x = -1 \)[/tex]:
[tex]\[
y = \frac{5(-1) + 18}{4} = \frac{-5 + 18}{4} = \frac{13}{4} = 3.25
\][/tex]
Thus, one point is [tex]\((-1, 3.25)\)[/tex].
For [tex]\( x = 0 \)[/tex]:
[tex]\[
y = \frac{5(0) + 18}{4} = \frac{18}{4} = 4.5
\][/tex]
Thus, another point is [tex]\((0, 4.5)\)[/tex].
For [tex]\( x = 1 \)[/tex]:
[tex]\[
y = \frac{5(1) + 18}{4} = \frac{5 + 18}{4} = \frac{23}{4} = 5.75
\][/tex]
Thus, another point is [tex]\((1, 5.75)\)[/tex].
4. Plot the points:
On a graph, plot the points [tex]\((-1, 3.25)\)[/tex], [tex]\((0, 4.5)\)[/tex], and [tex]\((1, 5.75)\)[/tex].
5. Draw the line:
After plotting these points, draw a straight line through them. If all points lie on the same line, you have correctly graphed the equation.
Given that the points are [tex]\((-1, 3.25)\)[/tex], [tex]\((0, 4.5)\)[/tex], and [tex]\((1, 5.75)\)[/tex], your graph should show a straight line passing through these three points.
