Pls help :( A city planner is rerouting traffic in order to work on a stretch of road. The equation of the path of the old route can be described as y = two fifthsx − 4. What should the equation of the new route be if it is to be parallel to the old route and will go through point (Q, P)?

y − Q = negative five halves(x − P)
y − Q = two fifths(x − P)
y − P = negative five halves(x − Q)
y − P = two fifths(x − Q)

Given:

Old route :

New route is parallel to the old route and will go through point (Q, P).

To find:

The equation of new route.

Solution:

Slope intercept form of a line is

where, m is slope and b is y-intercept.

On comparing , we get

Slope of is .

Slope of parallel lines are same. So, the slope of new route is also .

New route will go through point (Q, P) with slope , so the equation for new route is

where, m is slope.

Therefore, the correct option is D.

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)

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