Respuesta :
The equation in standard form of the line that passes through the given point and has the given slope and [tex]-4=\frac{1}{2}(-15)+b[/tex] 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,
[tex]-4=\frac{1}{2}(-15)+b[/tex] ---- 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,
[tex]m=\frac{1}{2}, x=-15, y=-4[/tex]
Which means that, line is passing through (-15, -4) at a slope of [tex]\frac{1}{2}[/tex]
Now, solve (1) for intercept,
Plugging in m = 1/2 and (x, y) = (-15, -4) we get,
[tex]\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}[/tex]
Then, the line equation in slope intercept form will be
[tex]y=\frac{1}{2} x+\frac{7}{2}[/tex]
Rearranging the terms to get standard form,
[tex]\rightarrow 2 y=x+7 \rightarrow x-2 y=-7[/tex]
hence, the line equation in standard form is x – 2y = - 7
