Math Problem Statement

Work out the gradient of the line on the graph below. Give any decimal answers to 1 d.p.

Solution

To calculate the gradient of the line in the graph, we follow these steps:

  1. Recall the formula for gradient: Gradient=ΔyΔx=y2y1x2x1\text{Gradient} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} where (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) are two points on the line.

  2. Pick two clear points from the graph:

    • From the graph, the line passes through (0,0)(0, 0) and (5,25)(5, 25).
  3. Substitute into the gradient formula: Gradient=y2y1x2x1=25050=255=5.0\text{Gradient} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{25 - 0}{5 - 0} = \frac{25}{5} = 5.0

  4. Final Answer: The gradient of the line is 5.0\mathbf{5.0}.

Let me know if you'd like me to elaborate further! 😊


Related Questions:

  1. What does a positive gradient indicate about a line's direction?
  2. How do you calculate the gradient for a horizontal line?
  3. How would the gradient change if the points were closer together but still on the same line?
  4. Can a gradient be a negative number? What does that represent?
  5. How does the gradient relate to the equation of the line?

Tip:

When identifying points on a graph to calculate the gradient, choose points where the line clearly crosses grid intersections to avoid inaccuracies.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Linear Functions
Gradients

Formulas

Gradient formula: m = (y2 - y1) / (x2 - x1)

Theorems

-

Suitable Grade Level

Grades 6-8