Question

Find the equation of the line of the form y= mx + b that passes through the following pairs of points.

1. (1, 2) and (3, 4)
2. (5,6) and (0,11)
3. (3,-1) and (7,-5)​

Answer 1

y = x + 1 is the equation for points (1, 2) and (3, 4) and for points (5, 6) and (0, 11). y = -x + 2 is the equation for points (3, -1) and (7, -5).

Step-by-step explanation:

To find the equation of a line in the form y = mx + b that passes through two given points, we need to first find the slope (m). The slope is calculated by taking the difference in y-coordinates divided by the difference in x-coordinates between the two points. Once we have the slope, we can substitute one of the given points and the slope into the equation and solve for the y-intercept (b).

Let's go through the steps for the three given pairs of points:

1. For points (1, 2) and (3, 4):
   Slope (m) = (4 - 2) / (3 - 1) = 2 / 2 = 1
   Using point (1, 2): 2 = 1(1) + b --> b = 1
   Therefore, the equation is y = x + 1.
2. For points (5, 6) and (0, 11):
   Slope (m) = (11 - 6) / (0 - 5) = -5 / -5 = 1
   Using point (5, 6): 6 = 1(5) + b --> b = 1
   Therefore, the equation is y = x + 1.
3. For points (3, -1) and (7, -5):
   Slope (m) = (-5 - (-1)) / (7 - 3) = -4 / 4 = -1
   Using point (3, -1): -1 = -1(3) + b --> b = 2
   Therefore, the equation is y = -x + 2.