Math Problem Statement

The equation of a straight line L is y = 3 - 4x. Write down the gradient of L.

Solution

To solve this question:

The equation given is y=34xy = 3 - 4x.

In this equation, the general form for a straight line is y=mx+cy = mx + c, where:

  • mm is the gradient (or slope) of the line,
  • cc is the y-intercept (the point where the line crosses the y-axis).

Comparing y=34xy = 3 - 4x to y=mx+cy = mx + c, we see that:

  • m=4m = -4.

Therefore, the gradient of line LL is -4.

Would you like further details or have any questions?

Here are some related questions for further practice:

  1. What is the y-intercept of the line y=34xy = 3 - 4x?
  2. How would you rewrite y=34xy = 3 - 4x in the form ax+by=cax + by = c?
  3. What is the gradient of a line parallel to y=34xy = 3 - 4x?
  4. How would you find the gradient of a line perpendicular to y=34xy = 3 - 4x?
  5. If y=34xy = 3 - 4x represents a road incline, what does a gradient of -4 indicate about its direction?

Tip: The gradient of a line indicates the steepness and direction of the slope; a negative gradient means the line slopes downwards.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Linear Equations
Gradients of Lines

Formulas

y = mx + c (slope-intercept form)

Theorems

-

Suitable Grade Level

Grades 7-9