Question

Graph two lines whose solution is (1,4)

Answer 1

The graph is shown below.

System:

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

Explanation:

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:

$m=3$

So:

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

SECOND LINE (THE BLUE ONE SHOWN BELOW):

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

$m=-1$

So:

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

So the two lines are:

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

Note.

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

$y=mx+b \\ \\ \\ m:Slope \\ \\ b:y-intercept$

Learn more:

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

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