given the line AB with A(1,4) and B(-3,-1) is parallel to line CD with C(8,3) and D(x,-7), solve for the missing value of x.

x = 0

Step-by-step explanation:

We can find the missing value by solving for the other points (graphically or algebraically). We would first find the line of Points A and B in order to find the parallel line that would help us find the coordinate point with the x-value.

1) Graph points A, B, and C.

2) Calculate the slope of points A and B by using the slope formula:

y2 - y1/x2 - x1.  

-1 - 4/-3 - 1The slope is 5/4.

3) Write 4 = 5/4(x) + b

**We get 4 from the point A (1, 4)

Plug 1 into x and solve for 4 in order to get your y-intercept.

4 = 5/4(1) + b

4 = 5/4 +b

**If 1 = 4/4, then 4 = 16/4.

16/4 = 5/4 + b

11/4 = b

2.75 = b

4) So our y-intercept is 2.75. We now have an equation of  y = 5/4x + 2.75 (graph it along with points A and B to see that it intersect both points.

5) Now we will use that line to find a line parallel to it. We know that if two lines have the same slope then they are parallel, so for the equation of the parallel line, we write: y = 5/4x + b so far.

6) We will find the y-intercept and use that to find the x-value of point D.

First we plug in the x and y values of point C to find the y-intercept

y = 5/4x + b --> 3 = 5/4(8) + b --> 3 = 40/4 + b --> 3 = 10 + b --> -7 = b

7) Now we have the equation of the line that is parallel to line AB: y = 5/4x -7

To find the missing value of x, plug the y-value of point D into the equation and solve for x.

--> -7 = 5/4x -7

--> x = 0

**You can double check this by graphing each point and both equations for the lines.

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