Math Problem Statement

Write an equation for the graph, where y depends on x.

Solution

The graph in the image shows a straight line, and we are asked to write the equation of the line where yy depends on xx.

To write the equation of a straight line, we use the slope-intercept form:

y=mx+by = mx + b

Where:

  • mm is the slope of the line, and
  • bb is the y-intercept (the point where the line crosses the y-axis).

Step 1: Identify the y-intercept (bb)

From the graph, the line crosses the y-axis at y=7y = 7, so:

b=7b = 7

Step 2: Calculate the slope (mm)

The slope mm is the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

From the graph, two clear points are:

  • (0,7)(0, 7) (the y-intercept)
  • (2,4)(2, 4)

The slope mm is calculated as follows:

m=riserun=4720=32m = \frac{\text{rise}}{\text{run}} = \frac{4 - 7}{2 - 0} = \frac{-3}{2}

Step 3: Write the equation

Now that we know the slope m=32m = -\frac{3}{2} and the y-intercept b=7b = 7, the equation of the line is:

y=32x+7y = -\frac{3}{2}x + 7

Would you like further clarification, or do you have any questions?

Here are five related questions for practice:

  1. What is the equation of a line with slope 12\frac{1}{2} and y-intercept 33?
  2. If the line passes through points (1,4)(1, 4) and (1,2)(-1, 2), how do you find its equation?
  3. How do you determine the slope of a line given its equation in standard form Ax+By=CAx + By = C?
  4. What is the slope of a line parallel to y=32x+7y = -\frac{3}{2}x + 7?
  5. How would the equation change if the line were shifted 3 units down?

Tip: When finding the slope, always carefully pick points where the line crosses grid intersections for more accurate calculations.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope-Intercept Form

Formulas

y = mx + b

Theorems

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Suitable Grade Level

Grades 8-10