Finding the Equation of a Line from a Graph: Kudzu Vine Growth

Published on March 10, 2026

Algebra

Determine the linear equation (y = mx + b) modeling the length of a kudzu vine over time by calculating the slope (rate of growth) and the y-intercept from the provided graph.

Question

Answer

The problem asks to write an equation for the function shown in the graph, in the form

. Here,

is the length of the vine in feet, and

is the number of days it grows.

Step 1: Find the y-intercept ().
The

-intercept is the point where the line crosses the

-axis (where

).
From the graph, when

, the value of

is 4.
Thus, the

-intercept

Step 2: Find the slope ().
The slope

represents the rate of change (growth per day) and can be calculated using two points

and

on the line:

We already have one point:

Let’s find another clear point on the line. The line appears to pass through

.
Let

Now, calculate the slope

The slope

Alternatively, we can check another point, such as

The slope is consistently

Step 3: Write the equation.
Substitute the values of

and

into the slope-intercept form

This simplifies to:

The required format is

.
The first box is for the slope (

), and the second box is for the

-intercept (

The equation for the function is:

Final Answer:
The equation is

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Finding the Equation of a Line from a Graph: Kudzu Vine Growth

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