To find the equation of the line in slope intercept form, we must have the slope and the y intercept. Finding the slope is easy:
[tex] m=\frac{y_2-y_1}{x_2-x_1} \implies \\ m= \frac{8-2}{4-6} = \\ \frac{6}{-2}=-3 [/tex]
So now we want the y intercept. We can use either points to do this, so for simplicity let's use the second one since the numbers are smaller. First of all, we have:
y=-3x+b. Plugging in 6 for x and 2 for y we have, 2=-18+b which means b=20. Checking our answer we have:
y=-3x+20 which means 8=-3*4+20, which is true. So our equation is indeed y=-3x+20
The equation of the line that passes through the given points is 3x + y = 20 OR y = -3x +20
From the question,
We are to write an equation of the line that passes through the points (4, 8) and (6, 2)
The formula for determining the equation of straight line with two given points, (x₁, y₁) and (x₂, y₂), is
[tex]\frac{y-y_{1} }{x-x_{1}} =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
From the question
x₁ = 4
y₁ = 8
x₂ = 6
y₂ = 2
Putting the values into the formula, we get
[tex]\frac{y-8}{x-4} =\frac{2-8}{6-4}[/tex]
Then,
[tex]\frac{y-8}{x-4} =\frac{-6}{2}[/tex]
[tex]\frac{y-8}{x-4} =-3[/tex]
This becomes
[tex]y -8 = -3(x-4)[/tex]
Clearing the brackets
[tex]y -8 = -3x + 12[/tex]
Now, add 8 to both sides
[tex]y-8+8 =-3x +12 +8[/tex]
Then, we get
[tex]y = -3x +20[/tex]
OR
[tex]3x+y =20[/tex]
Hence, the equation of the line that passes through the given points is 3x + y = 20 OR y = -3x +20
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