How do you solve #y=1/3x + 2# and #y=-4/3x -3# by graphing?

Question

Eva Adamson · Accepted Answer

(-3,1) is where they intersect

Find three sets of coordinates for the first line, plot these three points and join them together. Do the same for the second line and where the two lines cross will be the solution - an #x# value and a #y# value. If you solve it algebraically you can check your graphing is correct Equate both equations: #1/3x +2# = #-4/3x-3# Add #4/3x# to both sides: #5/3x +2=-3# Subtract 2 from both sides: #5/3x=-5# Divide both sides by#5/3#: #x=-3# Put #x=3# into either equation to find #y#: #y=(1/3)##xx#-3+2 #y=1#

Eva Adamson · Answer

undefined To solve the system of equations $y = \frac{1}{3}x + 2$ and $y = -\frac{4}{3}x - 3$ by graphing, plot both equations on the same graph and find the point(s) where they intersect.

Here's how you can do it:

1. For the first equation $y = \frac{1}{3}x + 2$:
   Plot the y-intercept at (0, 2).
   Use the slope of $1/3$ to find another point, like (3, 3).

2. For the second equation $y = -\frac{4}{3}x - 3$:
   Plot the y-intercept at (0, -3).
   Use the slope of $-4/3$ to find another point, like (3, -7).

3. Plot both lines on the same graph.

4. Find the point(s) where the lines intersect. This point represents the solution to the system of equations.

5. If the lines do not intersect, it means the system has no solution.

Graphing the equations will visually show the intersection point or points, providing the solution to the system of equations.