Determine the value of x so that the line containing the given points is parallel to another line whose slope is also given.

12. a(x, 5) and b(-4,3)
slope = -1

13. r(3, -5) and s(1, x)
slope = -2

Step-by-step explanation:

12) A(x, 5) and B(-4,3)

slope = -1

We want to determine the value of x so that the line AB is parallel to another line whose slope is given as -1

Slope, m is expressed as change in y divided by change in x. This means

Slope = (y2 - y1)/(x2 - x1)

From the information given

y2= 3

y1 = 5

x2 = -4

x1 = x

Slope = (3-5) / (-4-x) = -2/-4-x

Recall, if two lines are parallel, it means that their slopes are equal. Since the slope of the parallel line is -1, therefore

-2/-4-x = -1

-2 = -1(-4-x)

-2 = 4 + x

x = -2 - 4 = - 6

x = -6

13) R(3, -5) and S(1, x)

slope = -2

We want to determine the value of x so that the line RS is parallel to another line whose slope is given as -2

Slope = (y2 - y1)/(x2 - x1)

From the information given

y2= x

y1 = -5

x2 = 1

x1 = 3

Slope = (x - -5) / (1 - 3) = (x+5)/-2

Since the slope of the parallel line is -2, therefore

(x+5)/-2 = -2

x + 5 = -2×-2

x + 5 = 4

x = 4 - 5 = - 1