Math Problem Statement

Write the equation for the graphed line

Write the equation for the graphed line.

Solution

To find the equation of the line graphed in the image, we need to determine two key components: the slope and the y-intercept. The equation of a line in slope-intercept form is:

y=mx+by = mx + b

where:

  • mm is the slope,
  • bb is the y-intercept.

Step 1: Find the Slope (m)

The slope of a line is calculated as the change in yy divided by the change in xx between two points on the line:

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

From the image, two points on the line are:

  • (0,7)(0, 7)
  • (4,4)(4, 4)

Using these points: m=4740=34=34m = \frac{4 - 7}{4 - 0} = \frac{-3}{4} = -\frac{3}{4}

Step 2: Identify the y-Intercept (b)

The y-intercept is where the line crosses the y-axis. From the point (0,7)(0, 7), we can see that the line crosses the y-axis at y=7y = 7. Therefore, b=7b = 7.

Step 3: Write the Equation

Now that we know the slope m=34m = -\frac{3}{4} and the y-intercept b=7b = 7, we can write the equation of the line:

y=34x+7y = -\frac{3}{4}x + 7

Final Answer

The equation of the graphed line is: y=34x+7y = -\frac{3}{4}x + 7

Would you like a breakdown of how to apply this to other problems, or have any other questions?

Related Questions

  1. How do you find the equation of a line if only given two points?
  2. What are different forms of a linear equation (e.g., point-slope, standard form)?
  3. How would you graph a line given its equation?
  4. How can you find the x-intercept of a line from its equation?
  5. What are parallel and perpendicular slopes?

Tip

To check your answer, substitute one of the points into your equation to ensure it satisfies the line equation.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope-Intercept Form

Formulas

y = mx + b
Slope formula m = (y2 - y1) / (x2 - x1)

Theorems

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Suitable Grade Level

Grades 7-9