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Graph the linear equation. Find three points that solve the equation, then plot them on the graph.

[tex]\[ x - 4y = -18 \][/tex]



Answer :

GinnyAnswer
To graph the linear equation [tex]\(x - 4y = -18\)[/tex], we first need to find three points that satisfy this equation. Let's go through the process step-by-step:

1. Select an [tex]\(x\)[/tex]-value and solve for [tex]\(y\)[/tex]:

- For [tex]\(x = 0\)[/tex]:
[tex]\[ 0 - 4y = -18 \\ -4y = -18 \\ y = \frac{-18}{-4} \\ y = 4.5 \][/tex]
The point is [tex]\((0, 4.5)\)[/tex].

- For [tex]\(x = 4\)[/tex]:
[tex]\[ 4 - 4y = -18 \\ -4y = -22 \\ y = \frac{-22}{-4} \\ y = 5.5 \][/tex]
The point is [tex]\((4, 5.5)\)[/tex].

- For [tex]\(x = -4\)[/tex]:
[tex]\[ -4 - 4y = -18 \\ -4y = -14 \\ y = \frac{-14}{-4} \\ y = 3.5 \][/tex]
The point is [tex]\((-4, 3.5)\)[/tex].

2. Plot the Points:

Now we have three points: [tex]\((0, 4.5), (4, 5.5), (-4, 3.5)\)[/tex].

Plot these points on a coordinate plane.
- Point [tex]\((0, 4.5)\)[/tex] is on the y-axis at 4.5 units up.
- Point [tex]\((4, 5.5)\)[/tex] is 4 units right from the origin and 5.5 units up.
- Point [tex]\((-4, 3.5)\)[/tex] is 4 units left from the origin and 3.5 units up.

3. Draw the Line:

Once the three points are plotted, draw a straight line through these points. This line represents the graph of the linear equation [tex]\(x - 4y = -18\)[/tex].

By following these steps, the linear equation is accurately graphed, and the points [tex]\((0, 4.5), (4, 5.5), (-4, 3.5)\)[/tex] should be used for plotting.

We can solve the equation  x-4y = -18  for y in two ways:

Method 1: Isolate y

Isolate y: Add 4y to both sides of the equation to get x by itself:

x - 4y + 4y = -18 + 4y

x = -18 + 4y

Express y in terms of x: Now, x is alone on one side. We can rewrite the equation to show y by itself:

y = (x + 18) / 4

This means for any value of x, we can find the corresponding y by plugging x into this equation.

Method 2: Slope-Intercept Form

Rewrite in slope-intercept form: Move the constant term to the right side of the equation:

x - 4y = -18

-4y = -x - 18

Isolate y: Divide both sides by -4 (remember to flip the sign when dividing by a negative number):

y = (x + 18) / 4

This arrives at the same solution as method 1.

Finding Points on the Line:

While any value of x will give a corresponding y value, here are three specific points that lie on the line:

x = 0: If we plug x = 0 into the equation, we get y = (0 + 18) / 4 = 4.5. So one point is (0, 4.5).

x = 4: If we plug x = 4 into the equation, we get y = (4 + 18) / 4 = 5.5. So another point is (4, 5.5).

x = -4: If we plug x = -4 into the equation, we get y = (-4 + 18) / 4 = 3.5. So a third point is (-4, 3.5).

These points are plotted on the graph you saw.

View image Tangeryne

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