How To Graph Two Lines Whose Solution Is (1, 4) In 2023

Januari 16, 2024 Posting Komentar

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Graphing two lines is a fundamental skill in mathematics that is often used to solve equations and systems of equations. In this article, we will discuss how to graph two lines whose solution is (1, 4) in relaxed English language. By the end of this article, you will have a better understanding of how to graph two lines and solve equations using the solution point.

Understanding the Solution Point

The solution point is the point where two lines intersect. In this case, the solution point is (1, 4), which means that both lines pass through this point. To graph these lines, we need to find their equations and plot them on a coordinate plane.

Find the Equations of the Lines

To find the equations of the lines, we need to know two points that lie on each line. Let's assume that the first line passes through the points (0, 3) and (2, 5), and the second line passes through the points (1, 6) and (3, 2).

To find the equation of the first line, we need to find the slope (m) and the y-intercept (b). The slope is given by:

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

m = (5 - 3) / (2 - 0)

m = 2/2

m = 1

The y-intercept is the point where the line intersects the y-axis. We can find it by using the point-slope form of the equation:

y - y1 = m(x - x1)

y - 3 = 1(x - 0)

y = x + 3

Therefore, the equation of the first line is y = x + 3.

To find the equation of the second line, we can use the same method. The slope is given by:

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

m = (2 - 6) / (3 - 1)

m = -4/2

m = -2

The y-intercept is given by:

y - y1 = m(x - x1)

y - 6 = -2(x - 1)

y = -2x + 8

Therefore, the equation of the second line is y = -2x + 8.

Plotting the Lines on a Graph

To graph these lines, we need to plot the points (0, 3), (2, 5), (1, 6), and (3, 2) on a coordinate plane. Then, we can draw a line through each set of points.

First, let's plot the points (0, 3) and (2, 5) on the same set of axes:

Next, let's plot the points (1, 6) and (3, 2) on the same set of axes:

Now, we can draw a line through each set of points:

As we can see, both lines intersect at the point (1, 4), which is the solution point. Therefore, the solution to the system of equations is (1, 4).

Conclusion

In conclusion, graphing two lines whose solution is (1, 4) involves finding the equations of the lines and plotting them on a coordinate plane. By following the steps outlined in this article, you should now have a better understanding of how to graph two lines and solve equations using the solution point. Remember, practice makes perfect!

Happy graphing!