Math Problem Statement

The gradient of the following line is

The gradient of the following line is

Solution

The gradient (or slope) of a line can be calculated using the formula:

m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}

Here, we can see from the graph that one point on the line is (3,4)(3, -4). We can also assume that another point on the line passes through the origin, (0,0)(0, 0).

Using these two points, we apply the formula:

m=4030=43m = \frac{-4 - 0}{3 - 0} = \frac{-4}{3}

Thus, the gradient (slope) of the line is:

m=43m = -\frac{4}{3}

Would you like any further details or explanations?

Here are 5 related questions to expand your understanding:

  1. How would the slope change if the line passed through a different point?
  2. What is the equation of the line in slope-intercept form using this slope?
  3. How do you interpret a negative slope in terms of the line's direction?
  4. Can you calculate the length of the line segment between two points on this line?
  5. How would you find the x-intercept and y-intercept of this line?

Tip: The steeper the line, the larger the magnitude of the slope. Positive slopes rise from left to right, while negative slopes fall from left to right.

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Math Problem Analysis

Mathematical Concepts

Algebra
Analytic Geometry
Slope of a Line

Formulas

m = (y2 - y1) / (x2 - x1)

Theorems

Slope Formula

Suitable Grade Level

Grades 8-10