Graph two lines whose solution is (1,4)

In this case, we need to graph two lines whose solution is (1, 4). In other words, we need a system of linear equations in two variables that meet at the point of intersection (1, 4). So:

FIRST LINE (THE RED ONE SHOWN BELOW):

Let's say it has a slope of 3, so:

[tex]m=3[/tex]

So:

[tex]y=3x+b \\ \\ Since \ (1,4) \ is \ solution \ to \ this \ line, \ then: \\ \\ 4=3(1)+b \\ \\ b=4-3 \\ \\ b=1 \\ \\ \\ So, \ first \ line: \\ \\ y=3x+1[/tex]

SECOND LINE (THE BLUE ONE SHOWN BELOW):

Let's say it has a slope of -1, so:

[tex]m=-1[/tex]

So:

[tex]y=-x+b \\ \\ Since \ (1,4) \ is \ solution \ to \ this \ line, \ then: \\ \\ 4=-1+b \\ \\ b=4+1 \\ \\ b=5 \\ \\ \\ So, \ second \ line: \\ \\ y=-x+5[/tex]

So the two lines are:

[tex]\begin{array}{c}(1)\\(2)\end{array}\left\{ \begin{array}{c}y=3x+1\\y=-x+5\end{array}\right.[/tex]

Note.

Remember that the slope-intercept form of the equation of a line is:

[tex]y=mx+b \\ \\ \\ m:Slope \\ \\ b:y-intercept[/tex]

Learn more:

Graph of linear equations: https://brainly.com/question/13799715

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facundo3141592 facundo3141592 · Answer 2 · 2021-09-17T21:19:28+02:00

Here we want to create a system of linear equations, such that the solution of the system is the point (1, 4).

The lines I created are:

y = 1*x + 3

y = -6*x + 10

And the graph can be seen at the end of the answer.

We start with a general system:

y = a*x + b

y = c*x + d

We just want that both of these have the solution (1, 4)

This means that:

4 = a*1 + b

4 = c*1 + d

now is really trivial, for the first equation we can get:

4 = a*1 + b

First we define the value of one a, we can use a = 1

4 = 1*1 + b

4 = 1 + b

4 - 1 =b

3 = b

Now we got one of the lines:

y = 1*x + 3

Now for the other line:

4 = c*1 + d

We can define the value of d, for example let's take d = 10, then we get:

4 = c*1 + 10

4 - 10 = c*1

-6 = c

Then this other line is:

y = -6*x + 10

Then the system of lines is:

y = 1*x + 3

y = -6*x + 10

The graph of these two lines can be seen below:

If you want to learn more, you can read:

https://brainly.com/question/21404414