Question

4. Explain how to show that the line through points A(-2,-5) and B(-1,5) is parallel to the line that represents

the equation y=10x + 12.

Answer 1

The slope of the line through points A(-2,-5) and B(-1,5) is calculated to be 10, which matches the slope of the line y=10x + 12, proving the two lines are parallel because parallel lines have equal slopes.

Step-by-step explanation:

To show that the line through points A(-2,-5) and B(-1,5) is parallel to the line represented by the equation y=10x + 12, we first need to find the slope of the line through A and B. The slope can be found using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of points A and B respectively.

Applying the formula to our points A(-2,-5) and B(-1,5), we get (5 - (-5)) / (-1 - (-2)) = 10 / 1 = 10.

Since the slope of the line through A and B is 10, which is the same as the slope of the line y=10x + 12, we can conclude that both lines are parallel to each other because parallel lines have equal slopes.

Answer 2

Parallel lines have the same slope
Find the slope of points A and B
(y2 - y1)/ (x2-x1)
(5-(-5))/(-1-(-2)) = (5+5)/(-1+2) = 10/1
The slope of the points is 10
In the equation
y = 10x + 12
Y = mx + b, m indicating slope
The slope of the equation is also 10
Because both slope is 10, the line through the points and the equation is parallel