Question

Write an equation in standard form of the line that passes through the given point and has the given slope m

Answer 1

The equation in standard form of the line that passes through the given point and has the given slope and $-4=\frac{1}{2}(-15)+b$ is x – 2y = - 7

Solution:

Given that, We have write an equation in standard form of the line that passes through the given point and has the given slope "m"

Given equation is,

$-4=\frac{1}{2}(-15)+b$  ---- eqn 1

Here, if we observe the above given equation it is in the form of the slope – intercept form, i.e. y = mx + c

Where "m" is the slope of line and "c" is the y-intercept

So, now by comparison we get,

$m=\frac{1}{2}, x=-15, y=-4$

Which means that, line is passing through (-15, -4) at a slope of $\frac{1}{2}$

Now, solve (1) for intercept,

Plugging in m = 1/2 and (x, y) = (-15, -4) we get,

$\begin{array}{l}{\rightarrow-4=\frac{1}{2}(-15)+b} \\\\ {\rightarrow-4=\frac{-15}{2}+b} \\\\ {\rightarrow b=\frac{15}{2}-4=\frac{15-8}{2}} \\\\ {\rightarrow b=\frac{7}{2}}\end{array}$

Then, the line equation in slope intercept form will be

$y=\frac{1}{2} x+\frac{7}{2}$

Rearranging the terms to get standard form,

$\rightarrow 2 y=x+7 \rightarrow x-2 y=-7$

hence, the line equation in standard form is x – 2y = - 7