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)?

Jonas Bautista

Jonas Bautista

Answered question

2023-01-08

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)?

Answer & Explanation

Sailiaadvadesw95

Sailiaadvadesw95

Beginner2023-01-09Added 12 answers

The slope, or rate of change, is calculated as ΔyΔx, or y2y1x2x1. Plugging in, m=7521=2.
The initial value will then be discovered. A line's slope-intercept equation is y=mx+b, where m is the slope and b is the initial value. The slope was determined to be m = 2. The initial value of b will be provided by plugging our first point into the equation.
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.

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