Question

Complete the equation of the line through (1, 4) and (2, 2).
Use exact numbers.​

Answer 1

The equation of the line has the form y=mx+b

Let's create a system of equations

`\left \{ {{4=1m+b} \atop {2=2m+b}} \right. \\\left \{ {{-8=-2m-2b} \atop {2=2m+b}} \right. \\-6=-b\\b=6\\\\2=2m+6\\2m=-4\\m=-2`

the equation of the line through (1, 4) and (2, 2) is y=-2x+6

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Answer 2

`y = - 2x + 6`

Explanation:

`(4 - 2)/(1 - 2) = (2)/( - 1) = - 2 \\ gradient = - 2 \\ \\ y = mx + c \\ y = - 2 * 4 + c \\ - 2 = - 8 + c \\ - 2 + 8 = c \\ 6 = c \\ \\ y = mx + c \\ y = - 2x + 6`