Question

Find an equation of the line containing the given pair of points.
​(4​,1​) and ​(12​,8​) Solve for y.

Answer 1

To find the equation of the line containing the given pair of points, we can use the slope-intercept form of a linear equation:

y = mx + b,

where m is the slope of the line and b is the y-intercept.

First, let's find the slope (m) using the given points (4,1) and (12,8):

m = (y2 - y1) / (x2 - x1)
m = (8 - 1) / (12 - 4)
m = 7 / 8

Now, we can choose one of the given points (let's use (4,1)) and substitute the slope and the coordinates of that point into the slope-intercept form to find the y-intercept (b):

1 = (7/8)(4) + b
1 = 7/2 + b
b = 1 - 7/2
b = -5/2

Therefore, the equation of the line containing the given pair of points is:

y = (7/8)x - 5/2

To solve for y, you can simply replace x with any given value or variable and evaluate.