Question

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

Answer 1

Answer:

y = (-5/6)x + 4

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:

$m=\frac{y_2-y_1}{x_2-x_1}$

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:

$m=\frac{-1-14}{6-(-12)}=\frac{-15}{6+12}=\frac{-15}{18}=-\frac{5}{6}$

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

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

So, solving for y, we get:

$\begin{gathered} y-14=-\frac{5}{6}\cdot x-\frac{5}{6}\cdot12 \\ y-14=-\frac{5}{6}x-10 \\ y=-\frac{5}{6}x-10+14 \\ y=-\frac{5}{6}x+4 \end{gathered}$

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