Math Problem Statement

What is the equation of the line shown in the graph?

Solution

This is an image of a graph showing a straight line. From a quick observation, I can infer that:

  • The line has a negative slope (slants downward from left to right).
  • The x-axis ranges from -10 to 10, and the y-axis also ranges from -10 to 10.
  • The line intersects the y-axis at y=10y = 10 and the x-axis at x=10x = 10, which suggests the equation of the line might be y=x+10y = -x + 10.

To confirm this, let’s look at the key characteristics of the graph:

  1. Slope (m): The line is decreasing, so the slope is negative. Since it drops 10 units vertically for every 10 units it moves horizontally, the slope is m=1m = -1.
  2. Y-intercept (b): The line crosses the y-axis at (0,10)(0, 10), so b=10b = 10.

Thus, the equation of the line is likely: y=x+10y = -x + 10

Would you like to confirm the equation or explore other features of this graph?

Related Questions:

  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. How do you find the x-intercept of a line from its equation?
  4. Can we find the equation of a line if we know only two points?
  5. How does changing the slope affect the steepness of a line?

Tip:

When reading a graph, always identify the intercepts and use them to form the equation of the line. This makes it easier to analyze or predict other points on the line.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Coordinate Geometry

Formulas

y = mx + b (Slope-intercept form of a line)
Slope formula: m = (y2 - y1) / (x2 - x1)

Theorems

Slope-Intercept Theorem

Suitable Grade Level

Grades 7-10