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# Cartesian plane question

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Question:

Find the equation whose graph is shown below. Write your answer in standard form.

(Standard form is A (x) + B (y) =C, where A is positive, and A, B, and C are integers with the greatest common divisor 1.)

It seems I can't put any images or links, so I'll just list out some of the plots on this line:

(-5, -2), ( -1, -1), ( 3, 0).

Apr 8, 2024

#1
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Pick any two points, I chose (3, 0) and (-1, -1).

Calculate slope:

$$\frac{-1 - 0}{-1 - 3}=\frac{1}{4}$$

From slope-intercept form, you know the equation is

y = (1/4)x + b

Plug in any point to find b. I chose (3, 0)

0 = (1/4)*3 + b

b = -(3/4)

Therefore the equation is

y = (1/4)x - (3/4)

To get into the desired form, subtract (1/4)x from both sides then multiply by lcm

-(1/4)x + y = -(3/4)

x - 4y = 3, is the equation in standard form.

Apr 9, 2024

#1
+394
+2

Pick any two points, I chose (3, 0) and (-1, -1).

Calculate slope:

$$\frac{-1 - 0}{-1 - 3}=\frac{1}{4}$$

From slope-intercept form, you know the equation is

y = (1/4)x + b

Plug in any point to find b. I chose (3, 0)

0 = (1/4)*3 + b

b = -(3/4)

Therefore the equation is

y = (1/4)x - (3/4)

To get into the desired form, subtract (1/4)x from both sides then multiply by lcm

-(1/4)x + y = -(3/4)

x - 4y = 3, is the equation in standard form.

hairyberry Apr 9, 2024