Line A passes the points (-5,-13) and (1,-1). Line B runs perpendicular to Line A and passes the points (6,5). Find the equation of each line.

passes through I assume.

slope of A = (-1 +13) / (1+5)

= 12/6 = 2
y = 2 x + b
put either point in to find b

so
slope of B = -1/slope of A = -1/2

so
5 = -(1/2)(6) + b
5 = -3 + b
b = 8
so
y = -x/2 + 8
2 y = -x + 16

how did you get the slope of -1/ slope of A=-1/2?Is the slope of line a is 2?

That is the correct answer

To find the equation of a line, we generally use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.

Let's start by finding the equation of Line A. We have two points on Line A: (-5, -13) and (1, -1). We will use the point-slope form and the formula to compute the slope.

Step 1: Find the slope of Line A.
The slope, denoted as m, can be calculated using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given coordinates.
Using (-5, -13) and (1, -1):
m = (-1 - (-13)) / (1 - (-5))
= 12 / 6
= 2

So, the slope of Line A is 2.

Step 2: Choose one point on Line A to substitute into the point-slope form.
Let's choose the point (-5, -13) to substitute for (x1, y1) in the point-slope form.

Step 3: Write the equation of Line A using the point-slope form.
Using the point-slope form, we have:
y - y1 = m(x - x1)
y - (-13) = 2(x - (-5))
y + 13 = 2(x + 5)
y + 13 = 2x + 10

Rearranging, we get:
y = 2x + 10 - 13
y = 2x - 3

So, the equation of Line A is y = 2x - 3.

Now, let's move on to finding the equation of Line B.

Step 1: Find the slope of Line B.
Since Line B is perpendicular to Line A, we know that the product of their slopes is -1. Therefore, the slope of Line B will be the negative inverse of the slope of Line A. The slope of Line A is 2, so the slope of Line B will be -1/2.

Step 2: Choose one point on Line B to substitute into the point-slope form.
We have the point (6, 5) on Line B. Let's use this point as (x1, y1) in the point-slope form.

Step 3: Write the equation of Line B using the point-slope form.
Using the point-slope form, we have:
y - y1 = m(x - x1)
y - 5 = (-1/2)(x - 6)
y - 5 = (-1/2)x + 3
y = (-1/2)x + 3 + 5
y = (-1/2)x + 8

So, the equation of Line B is y = (-1/2)x + 8.