Math Problem Statement

Geef bij de onderstaande grafieken de richtingscoëfficiënt en het startgetal.

Solution

The problem asks for the slope (richtingscoëfficiënt) and y-intercept (startgetal) of each of the given graphs.

General Equation of a Line:

y=mx+by = mx + b Where:

  • mm is the slope (richtingscoëfficiënt)
  • bb is the y-intercept (startgetal)

Step-by-Step Analysis:

Graph A:

  • The line decreases, so the slope is negative.
  • The y-intercept is at b=3b = 3.
  • To find the slope: It moves down 1 unit for every 1 step rightm=1m = -1.
  • Equation: y=x+3y = -x + 3.

Graph B:

  • The line increases, so the slope is positive.
  • The y-intercept is at b=3b = -3.
  • The slope appears to be 1, as it moves up 1 and right 1.
  • Equation: y=x3y = x - 3.

Graph C:

  • The line decreases, so the slope is negative.
  • The y-intercept is at b=3b = 3.
  • The slope is -1, since the line moves down 1 and right 1.
  • Equation: y=x+3y = -x + 3.

Graph D:

  • The line increases, so the slope is positive.
  • The y-intercept is at b=3b = -3.
  • The slope appears to be 1.
  • Equation: y=x3y = x - 3.

Summary of Equations:

  • A: y=x+3y = -x + 3
  • B: y=x3y = x - 3
  • C: y=x+3y = -x + 3
  • D: y=x3y = x - 3

Would you like a more detailed breakdown for any graph?


Related Questions:

  1. How do you calculate the slope using two points?
  2. What does the slope represent in real-world problems?
  3. How do you find the equation of a line given two points?
  4. What happens if the slope is zero or undefined?
  5. How can we determine if two lines are parallel or perpendicular?

Math Tip:

The slope mm is calculated using: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1} This helps when identifying equations from graphs!

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope
Y-intercept
Graphing Lines

Formulas

y = mx + b

Theorems

Slope formula

Suitable Grade Level

Grades 7-9