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. (4 points)

Part B: Make tables to find the solution to 2−x = 4x + 3. Take the integer values of x only between −3 and 3. (4 points)

Part C: How can you solve the equation 2−x = 4x + 3 graphically? (2 points)

Question

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. (4 points)

Part B: Make tables to find the solution to 2−x = 4x + 3. Take the integer values of x only between −3 and 3. (4 points)

Part C: How can you solve the equation 2−x = 4x + 3 graphically? (2 points)

imstuck · Answer

They are solutions for the equations because, in the coordinate plane AND in a table of x and y values, these 2 lines share the same coordinates.  Do you ha to solve them to see that the point is the same?

imstuck · Answer

Part B has you show that this is true.  It tells you to make a table for each equation.  In each of those tables, you will find that there is a point that both of the lines share.  That is called the solution, where the 2 lines cross.

imstuck · Answer

Actually, that first question is a little trickier than I first explained.  I didn't read it all the way through.  We have 2 equations that are set to equal y.  If the first equation = y, and the second equation = y, then the first equation equals the second equation because they are both equal to the same thing (y).  That is why the x coordinates are solutions of that longer equation.  That longer equation is just the first equation they gave you set equal to the second one.  When you solve it for x, that x makes both of the equations true.  Then you can find y from there.