Math Problem Statement

What is the equation of the straight line shown on the graph?

Solution

Let's analyze the image to find the equation of the straight line.

From the graph, we can identify two key aspects of the straight line:

  1. Slope: The slope (m) of the line is the ratio of the change in RR to the change in ss. Looking at the graph, we see that as ss increases by 6 (from 0 to 6), RR decreases by 9 (from 6 to -3). Thus, the slope is: m=ΔRΔs=96=32m = \frac{\Delta R}{\Delta s} = \frac{-9}{6} = -\frac{3}{2}

  2. Intercept: The intercept (where the line crosses the RR-axis) is at R=6R = 6, which gives us the y-intercept (c).

So, the equation of the line is: R=32s+6R = -\frac{3}{2}s + 6

Looking at the answer choices in the image, the correct answer is: R=32s+6R = -\frac{3}{2}s + 6

Do you have any questions, or would you like more details on this?

Here are some related questions for further exploration:

  1. How do you calculate the slope of a line from a graph?
  2. What is the significance of the y-intercept in a linear equation?
  3. Can the slope of a line ever be positive? What would that look like on a graph?
  4. How do you rewrite the equation of a line if you are given different points?
  5. What is the general form of a linear equation in two variables?

Tip: To easily find the slope of a line, pick two clear points on the graph, and use the formula change in ychange in x\frac{\text{change in y}}{\text{change in x}}.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Graphing

Formulas

Slope formula: m = (change in y) / (change in x)
Linear equation: y = mx + c

Theorems

Slope-Intercept Form

Suitable Grade Level

Grades 8-10