Graph and then find the solution for y=-1/2x-6

1 answer

To solve the equation \( y = -\frac{1}{2}x - 6 \), we'll first graph the equation and then find the solution points.

Step 1: Identify the components for graphing

The equation is in slope-intercept form \( y = mx + b \), where:

  • \( m \) is the slope, which is \( -\frac{1}{2} \).
  • \( b \) is the y-intercept, which is \( -6 \).

Step 2: Plot the y-intercept

Start by plotting the y-intercept:

  • The y-intercept is at \( (0, -6) \).

Step 3: Use the slope to find another point

From the y-intercept, apply the slope:

  • The slope \( -\frac{1}{2} \) means that for each 2 units you move to the right (positive x-direction), you move down 1 unit (negative y-direction).

Starting from the point \( (0, -6) \):

  • Move 2 units to the right to \( (2, -6) \).
  • Move 1 unit down to \( (2, -7) \).

Thus, the second point is \( (2, -7) \).

Step 4: Draw the graph

Plot both points \( (0, -6) \) and \( (2, -7) \) on a graph and draw a straight line through them. This line represents the equation \( y = -\frac{1}{2}x - 6 \).

Step 5: Finding solutions

Since the equation describes a line, any point \( (x, y) \) that lies on this line is a solution to the equation.

If you want specific values of \( x \) and \( y \), you can choose any \( x \) value and solve for \( y \):

  • Example 1: If \( x = 0 \): \[ y = -\frac{1}{2}(0) - 6 = -6 \] So, \( (0, -6) \) is a solution.

  • Example 2: If \( x = 2 \): \[ y = -\frac{1}{2}(2) - 6 = -1 - 6 = -7 \] So, \( (2, -7) \) is a solution.

  • Example 3: If \( x = 4 \): \[ y = -\frac{1}{2}(4) - 6 = -2 - 6 = -8 \] So, \( (4, -8) \) is another solution.

Conclusion

The graph is a straight line with a negative slope and a y-intercept at \( -6 \). Any point on this line is a solution to the equation \( y = -\frac{1}{2}x - 6 \).

Similar Questions
  1. 55. Find an equation of the tangent line to the graph off(x) =x^3 - 2x + 1 a) at (2,5); b) at (-1,2); c) at (0,1). I believe the
    1. answers icon 2 answers
  2. Rose wants to solve the equation 12(15x + 6.8) = 5(4 + 0.7x ). She uses a graphing program to graph the equations y = 12 (15x +
    1. answers icon 1 answer
  3. Graph the solution of each compound inequality.f > -1 and f < 5 Does this mean I just graph those 2 or solve them and find the
    1. answers icon 2 answers
  4. consider the polar graph §æ =(2/3)¦Ð. (¦Ð=pie)find the value of N such that r=N§æ, where 0¡Ü §æ ¡ÜN¦Ð has a)no
    1. answers icon 0 answers
more similar questions