What is the rate of change, the initial value, and the equation of the line that goes through the points #(1, 5)# and #(2,7)#?

1 Answer
Apr 6, 2018

Rate of Change: 2
Initial Value: 3
Equation: #y = 2x + 3#

Explanation:

The rate of change, or the slope, is calculated as #(Delta y) / (Delta x)#, or #(y_2 - y_1) / (x_2 - x_1)#. Plugging in, #m = (7 - 5) / (2 - 1) = 2#.

We'll next find the initial value. The slope-intercept equation of a line is #y = mx + b#, where #m# is the slope and #b# is the initial value. We have found the slope as # m = 2#. We will plug our first point into the equation to give us #b#, the initial value.

Point: (1, 5)
Equation: #y = 2x + b#

Plug In:
#y = 2x + b#
#5 = 2(1) + b#
#5 = 2 + b#
#3 = b#

Thus, our initial value is #b = 3#. This value, with our slope, gives us the equation: #y = 2x + 3#.