Math Problem Statement

Work out the equation of the straight line given in the diagram below. Calculate the gradient of the line, state the y-intercept, and write the equation in the form y = mx + c.

Solution

The image provided contains a question regarding finding the equation of a straight line based on the given graph.

Here's a summary of the steps:

  1. Calculate the gradient of the line: Two points on the line are given: (0, 4) and (2, 8). The gradient (slope) formula is: m=y2y1x2x1=8420=42=2m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 4}{2 - 0} = \frac{4}{2} = 2 So, the gradient m=2m = 2.

  2. State the y-intercept of the straight line: The y-intercept occurs when x=0x = 0. From the point (0, 4), we see that the y-intercept is 4.

  3. Write the equation of the line in the form y=mx+cy = mx + c: Using the gradient m=2m = 2 and the y-intercept c=4c = 4, the equation of the line is: y=2x+4y = 2x + 4

This is the required equation of the straight line.

Would you like any additional details or clarifications on this? Here are five relative questions:

  1. How do we generalize the equation of any straight line?
  2. What does the gradient represent geometrically on a graph?
  3. Can you explain why the y-intercept occurs when x=0x = 0?
  4. How would the equation change if the line had a negative gradient?
  5. How do we find the x-intercept from the equation of a straight line?

Tip: When finding the gradient of a line, always ensure you're using two distinct points on the line and applying the formula correctly to avoid sign errors.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Gradient (m) formula: m = (y2 - y1) / (x2 - x1)
Linear equation: y = mx + c

Theorems

Slope-Intercept Form of a Line

Suitable Grade Level

Grades 8-10