Question

Lines m and n are drawn in the coordinate plane. The equation of line m is y=-3x+8 and line n goes through point (-4,-11). When a transversal of the two lines is constructed the alternate interior angles formed by the transversal are congruent. What is the equation of line n?

Answer 1

Answer:

The equation of line n is;

y = -3x - 23

Step-by-step explanation:

Here, we want to find the equation of line n

For the alternate interior angles to be congruent after drawing the transversal, then both lines must be parallel

If the two lines are parallel, then their slopes are equal

To get the slope of line m, we compare the equation of line m to the standard form

The equation of line m is y = -3x + 8

if we compare this with the standard form which is y = mx + c

Then the slope of line m is -3 and since they are parallel lines, the slope of line n is -3 too

So now, we need to get the equation of line n

It passes through (-4,-11)

What we have already is;

y = -3x + c

we need to get the y-intercept to write the complete equation

To get the y-intercept we simply substitute for (-4,-11)

Thus, we have

-11 = -3(-4) + c

-11 = 12 + c

c = -11-12 = -23

The equation of line n is;

y = -3x - 23