Question

Plans for a stadium are drawn on a coordinate grid. One wall lies on the line y=2x+3. A perpendicular wall passes through the point (4,-7). Write the equation of the line that contains the new wall

Answer 1

the 1st wall lies on the line y = 2x+3

the new wall lies PERPENDICULAR to that one, and we want to know what equation would it be that makes that new wall's line

so, we really have 2 walls, the old and the new one, the new perpendicular
so we can say for each, we really have 2 equations

one is y = 2x+3
the other we dunno it, all we know about that one is that
is perpendicular to y = 2x+3, and passes through (4, -7)

so 2 lines, perpendicular to each other

keeping in mind that perpendicular lines have NEGATIVE RECIPROCAL slopes
what would be the slope of y = 2x+3 ?

Answer 2

2?

Answer 3

yes

Answer 4

so, if the slope of y = 2x+3, the slope of a line perpendicular to that will be

RECIPROCAL of 2
1/2

NEGATIVE of that
-1/2

so now we know, that it has a slope of -1/2 and passes through the point (4, -7)

let us use the point-slope form of a linear equation, to plug those points in and get the equation :)

point-slope form \(\large{ \implies y-y_1=m(x-x_1)\\ \quad \\


slope=m= -\cfrac{1}{2}\qquad \qquad \begin{array}{llll}
&x_1&y_1\\(&4\quad ,\quad &-7)
\end{array}\\ \quad \\

y-y_1=m(x-x_1)\implies y-(-7)=-\cfrac{1}{2}(x-(4))}\)

Answer 5

just solve for "y" to get the equation

Answer 6

So you would get y=-1/2x-5

Answer 7

yeap

Answer 8

Awesome thanks

Answer 9

yw