Question

Find an equation of the line containing the given pair of points.
​(4​,1​) and ​(12​,6​)

Answer 1

To find the equation of the line containing the given pair of points, we can use the formula for the equation of a line in slope-intercept form: y = mx + b.

First, let's find the slope (m) of the line using the formula m = (y2 - y1)/(x2 - x1), where (x1, y1) = (4, 1) and (x2, y2) = (12, 6):

m = (6 - 1)/(12 - 4) = 5/8

Now that we have the slope, we can choose one of the given points (let's use (4, 1)) and substitute it into the equation y = mx + b to find the y-intercept (b):

1 = (5/8)(4) + b
1 = 20/8 + b
1 = 5/2 + b
1 - 5/2 = b
-3/2 = b

So the y-intercept (b) is -3/2.

Now we can write the equation of the line y = mx + b using the slope (m = 5/8) and the y-intercept (b = -3/2):

y = (5/8)x - 3/2

Therefore, the equation of the line containing the given pair of points (4, 1) and (12, 6) is y = (5/8)x - 3/2.