Math Problem Statement

what points do i plot

What points do I plot?

Solution

To plot the lines represented by the equations on the graph, we need to identify a couple of points for each line.

Equation 1: y=16x+7y = -\frac{1}{6}x + 7

This equation is in slope-intercept form, y=mx+by = mx + b, where:

  • Slope (mm) = 16-\frac{1}{6}
  • Y-intercept (bb) = 7
  1. Plot the y-intercept at (0,7)(0, 7).
  2. Use the slope to find a second point. Since the slope is 16-\frac{1}{6}, go down 1 unit and right 6 units from the y-intercept.
    • Starting from (0,7)(0, 7), moving down 1 unit and right 6 units takes us to (6,6)(6, 6).

So, plot the points (0,7)(0, 7) and (6,6)(6, 6) for this line.

Equation 2: y=2x6y = 2x - 6

This equation is also in slope-intercept form, where:

  • Slope (mm) = 2
  • Y-intercept (bb) = -6
  1. Plot the y-intercept at (0,6)(0, -6).
  2. Use the slope to find a second point. Since the slope is 22, go up 2 units and right 1 unit from the y-intercept.
    • Starting from (0,6)(0, -6), moving up 2 units and right 1 unit takes us to (1,4)(1, -4).

So, plot the points (0,6)(0, -6) and (1,4)(1, -4) for this line.

Solution

Once you plot both lines on the graph, the point where they intersect is the solution to the system of equations.

Let me know if you'd like a further breakdown or if you have additional questions!


Here are some related questions you might find helpful:

  1. How do you find the intersection point algebraically for these two equations?
  2. What is the significance of the slope in each equation?
  3. How can you verify the solution after finding the intersection point?
  4. How do you interpret systems of equations with no solutions or infinite solutions?
  5. How would the graph look if one of the slopes was zero?

Tip: Always start by plotting the y-intercept when graphing linear equations; it’s the easiest point to locate on the graph.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Graphing

Formulas

Slope-intercept form y = mx + b

Theorems

Graphical method of solving systems of linear equations

Suitable Grade Level

Grades 8-10