Find a general form equation for the line through the pair of points?

Question

$(- 7, - 2)$ $(-7,-2)$ and $(1, 6)$ $(1,6)$

1567 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-15T16:37:26

$y = x + 5$ $y=x+5$

The general form of a line is $y = k x + m$ $y=kx+m$ where $k, m$ $k,m$ are real numbers.

To find $k$ $k$ which is how steep the line is. We'll use the formula $k = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $k={y_2-y_1}/{x_2-x_1}$ .

$(- 7, - 2), (1, 6)$ $(-7, -2), (1,6)$

Plug these values into the formula. Note how the first number in the parentheses represents the $x$ $x$ value and the second $y$ $y$ .

$k = \frac{6 - (- 2)}{1 - (- 7)} = \frac{6 + 2}{1 + 7} = \frac{8}{8} = 1$ $k={6-(-2)}/{1-(-7)}={6+2}/{1+7}=8/8=1$

Insert $k$ $k$ into $y$ $y$

$y = 1 \cdot x + m$ $y=1*x+m$

Finally, use one of the points to find $m$ $m$ , by inserting the $(x, y)$ $(x,y)$ pair into $y$ $y$ . I'll use the second as i think its eaiser.

$6 = 1 \cdot (1) + m \Rightarrow m = 5$ $6=1*(1)+m=>m=5$

Therefore, $y = x + 5$ $y=x+5$