Respuesta :
Answer:
The equation is y=-x+6.
Step-by-step explanation:
To find the slope of this equation, we use the equation m=y2-y1/x2-x1, where m is the slope. Take one y coordinate and subtract it from the other and do the same with the x coordinates. Then, divide the difference of the y coordinates by the difference of the x coordinates. For example, 6-2/0-4. This gets us 4/-4. You can also do 2-6/4-0 which gets us -4/4. No matter what, we get -1 for each (we don't include the 1 in front of the x). To find the y-intercept, plug in the coordinates. For example, do 6=0(-1)+b or 2=4(-1)+b. No matter which you use, you get an answer of b=6. This gives you an equation of y=-x+6. Hope this helps :)
The equation of the line that passes through the points (4,2) and (0,6) is y = 6 - x
To determine the equation for the line that passes through the points (4,2) and (0,6),
We will use the formula for the determining the equation of a line with two given points
The formula for the determining the equation of a line with two given points is
[tex]\frac{y-y_{1} }{x-x_{1} }=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
The given points are (4,2) and (0,6)
Therefore,
x₁ = 4
y₁ = 2
x₂ = 0
y₂ = 6
Now, putting these into the formula,
We get
[tex]\frac{y-2}{x-4}=\frac{6-2}{0-4}[/tex]
This becomes
[tex]\frac{y-2}{x-4}=\frac{4}{-4}[/tex]
[tex]\frac{y-2}{x-4}=-1[/tex]
Then, the equation becomes
[tex]y-2 = -1(x-4)[/tex]
[tex]y-2 = -x +4[/tex]
[tex]y = 4+2-x[/tex]
[tex]y = 6-x[/tex]
Hence, the equation of the line that passes through the points (4,2) and (0,6) is y = 6 - x
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