Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 2−x and y = 4x + 3 intersect are the solutions of the equation 2−x = 4x + 3.
Part B: Make tables to find the solution to 2−x = 4x + 3. Take the integer values of x only between −3 and 3.
Part C: How can you solve the equation 2−x = 4x + 3 graphically?
There seems to be a lot of people needing help in Algebra 1.
clearly, y=y
now substitute in the two different definitions.
Draw the two lines. The solution is where they intersect.
Your explanation is not very well done. Thank you for your time though :)
Part A: To find the x-coordinates of the points where the graphs of the equations y = 2−x and y = 4x + 3 intersect, we need to find the values of x that satisfy both equations.
Since the y-values are the same at the points of intersection, we can equate the two equations and solve for x.
So, we set y = 2−x equal to y = 4x + 3:
2−x = 4x + 3
Now we have an equation with x on both sides. To solve for x, we can apply algebraic techniques like combining like terms, moving terms to one side, and isolating x.
Part B: To find the solution to 2−x = 4x + 3 using tables, we can create a table and substitute integer values of x between -3 and 3 into the equation.
Let's create a table:
| x | 2−x | 4x + 3 |
|----|-------|----------|
| -3 | 5 | -9 |
| -2 | 4 | -5 |
| -1 | 3 | -1 |
| 0 | 2 | 3 |
| 1 | 1 | 7 |
| 2 | 0 | 11 |
| 3 | -1 | 15 |
By substituting the values of x into the equation, we can find the corresponding values of 2−x and 4x + 3, which helps us identify the solution to the equation.
Part C: To solve the equation 2−x = 4x + 3 graphically, we can plot the graphs of both equations on the same set of axes and look for their point of intersection.
First, we graph the equation y = 2−x. This is a line with a y-intercept of 2 and a slope of -1.
Next, we graph the equation y = 4x + 3. This is a line with a y-intercept of 3 and a slope of 4.
We then look for the point where the two graphs intersect. The coordinates of this point represent the solution to the equation 2−x = 4x + 3.