How can you solve the equation 4−x = 2x + 3 graphically?

x = 1/3

Step-by-step explanation:

Hello,

we can draw the two lines defined by

   y = 4 - x

   y = 2x + 3

And search for the intersection point as below

This is the point A (1/3, 11/3)

Do not hesitate if you have any question

Thanks

Step-by-step explanation:

Graph the two lines separately but on the same graph paper, and then from the completed graph read off the coordinates of the point of intersection.

y = 4 - x has a y-intercept of 4 and a slope of -1.  Plot the point (0, 4) and then draw a line with slope -1 through it.

y = 2x + 3 has a y-intercept of 3 and a slope of 2.  Plot (0, 3) and then draw a line with slope +2 through it.  

As a check, solve for x and y algebraically:

4 - x = 2x + 3 becomes 1 - x = 2x, or 3x = 1.  Then x = 1/3.

Use y = 4 - x to find the y value when x = 1/3:

y = 4 - 1/3 = 11/3

Thus, the solution is (1/3, 11/3)

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer