Part C: How can you solve the equation 8x = 2x + 2 graphically?
after you simplify , you get:
6x = 2
x = 2/6 = 1/3
In general, the equation of a line describes the relationship that the x and the y have for each ordered pair on the line.
e.g. if we had y = 2x + 1, that would mean that for every x value that you choose, the y will be one more than twice your x --> (3,7) or (-5, -9)
in your case we ended up saying that x = 1/3, and no mention was made of y.
so any ordered pair will do as long as your x value is 1/3.
e.g. (1/3 , 2) , (1/3, 5) , (1/3 , -4)
if you plot these points you will get a vertical line so that for every point on it, the x is 1/3
similarly if you ended up with something like y = 2, (where there is no x in your equation), you would have a horizontal line , and every point on that horizontal line has a y value of 2
Thank you
To solve the equation 8x = 2x + 2 graphically, you will need to plot the graphs of the two sides of the equation, which are 8x and 2x + 2, and find the point(s) of intersection.
Here are the steps to solve it graphically:
1. Start by rearranging the equation to get it in the form y = mx + b, where y represents the dependent variable (8x or 2x + 2), x represents the independent variable, m represents the slope, and b represents the y-intercept.
- For 8x, divide both sides by 8 to get x = (1/8)x + (1/4), so y = (1/8)x + (1/4).
- For 2x + 2, subtract 2x from both sides to get 0 = 2x + 2 - 2x, so y = 2.
2. Plot the graph of y = (1/8)x + (1/4), which is a straight line with a positive slope of 1/8 and a y-intercept of (0, 1/4).
3. Plot the graph of y = 2, which is a horizontal line passing through the y-axis at y = 2.
4. Look for the point(s) of intersection between the two graphs. The x-coordinate(s) of the point(s) of intersection will be the solution(s) to the equation.
5. If there is one point of intersection, read the x-coordinate from the graph, and that is the solution to the equation. If there is no point of intersection, then the equation has no solution.
Note: You can use a graphing calculator or software to quickly plot the graphs and find the point(s) of intersection.