To graph the equation by plotting three points, we'll first rearrange the given equation into a more familiar form, which is the slope-intercept form [tex]\(y = mx + b\)[/tex]. This will help us easily find points on the line.
Given equation:
[tex]\[
-4y = -5x - 18
\][/tex]
1. Divide both sides of the equation by -4 to solve for [tex]\(y\)[/tex]:
[tex]\[
y = \frac{-5}{-4}x + \frac{-18}{-4}
\][/tex]
2. Simplify the fractions:
[tex]\[
y = \frac{5}{4}x + 4.5
\][/tex]
Now that we have the equation in the form [tex]\(y = mx + b\)[/tex], let's find three points that lie on this line. We will choose three different values for [tex]\(x\)[/tex] and calculate the corresponding [tex]\(y\)[/tex] values.
Let's choose [tex]\(x = -4\)[/tex], [tex]\(x = 0\)[/tex], and [tex]\(x = 4\)[/tex].
### For [tex]\(x = -4\)[/tex]:
[tex]\[
y = \frac{5}{4}(-4) + 4.5
\][/tex]
[tex]\[
y = -5 + 4.5
\][/tex]
[tex]\[
y = -0.5
\][/tex]
So, one point is [tex]\((-4, -0.5)\)[/tex].
### For [tex]\(x = 0\)[/tex]:
[tex]\[
y = \frac{5}{4}(0) + 4.5
\][/tex]
[tex]\[
y = 0 + 4.5
\][/tex]
[tex]\[
y = 4.5
\][/tex]
So, another point is [tex]\((0, 4.5)\)[/tex].
### For [tex]\(x = 4\)[/tex]:
[tex]\[
y = \frac{5}{4}(4) + 4.5
\][/tex]
[tex]\[
y = 5 + 4.5
\][/tex]
[tex]\[
y = 9.5
\][/tex]
So, the third point is [tex]\((4, 9.5)\)[/tex].
In summary, the three points we have are:
- [tex]\((-4, -0.5)\)[/tex]
- [tex]\((0, 4.5)\)[/tex]
- [tex]\((4, 9.5)\)[/tex]
Plot these points on the coordinate plane. Once the points [tex]\((-4, -0.5)\)[/tex], [tex]\((0, 4.5)\)[/tex], and [tex]\((4, 9.5)\)[/tex] are plotted, connect them with a straight line. This line represents the graph of the equation [tex]\( -4y = -5x - 18 \)[/tex].
Click "Done" once you have plotted all points and the line should appear correctly on your graph.
