Question

(-12, 14) and (6,-1) linear equationswriting linear equations given two points.

Answer 1

y = (-5/6)x + 4

Step-by-step explanation:

The equation of a line can be calculated as:

`y-y_1=m(x-x_1)`

Where (x1, y1) is one point in the line and m is the slope and can be calculated as:

`m=(y_2-y_1)/(x_2-x_1)`

Where (x2, y2) is another point in the line.

So, replacing (x1, y1) by (-12, 14) and (x2, y2) by (6, -1), we get that the slope is equal to:

`m=(-1-14)/(6-(-12))=(-15)/(6+12)=(-15)/(18)=-(5)/(6)`

Then, with a slope equal to -5/6 and the point (-12, 14), we get that the equation of the line is:

`\begin{gathered} y-14=-(5)/(6)(x-(-12)) \\ y-14=-(5)/(6)(x+12) \end{gathered}`

So, solving for y, we get:

`\begin{gathered} y-14=-(5)/(6)\cdot x-(5)/(6)\cdot12 \\ y-14=-(5)/(6)x-10 \\ y=-(5)/(6)x-10+14 \\ y=-(5)/(6)x+4 \end{gathered}`

Therefore, the answer is y = (-5/6)x + 4