I struggle with connecting graphs of linear equation with algebraic form like $x+y=p$.
How do I develop the intuition that it represents a line that is sloping down and passes through value $p$ on $y$-axis in $XY$ plane?
$\begingroup$
$\endgroup$
1
-
2$\begingroup$ This question currently looks like it's more appropriate for Mathematics Stack Exchange. If it's about teaching graphs of linear equations, please edit to make that clearer. $\endgroup$– J WCommented Aug 28, 2023 at 6:20
Add a comment
|
2 Answers
$\begingroup$
$\endgroup$
2
Better to write it as y=-x+p you see that at x=0 y=p and x=p y=0 so for p>0 it goes down from (0,p) to (p,0) if p<0 it goes down from (0,p)to (p,0)
-
$\begingroup$ sign of p is not that important because it does not affect the slope of line rather operation between "x" & "y" is important as it affects the slope of line... $\endgroup$ Commented Aug 27, 2023 at 5:30
-
$\begingroup$ so just look at the sing of x in the form y=... and you see the slope down, if the sign is negative. $\endgroup$– trulaCommented Aug 27, 2023 at 13:26
$\begingroup$
$\endgroup$
Write it as $y = p + (-1) x.$
Along the $y$-axis, $x$ is $0,$ so the $y$-value is $p.$
The $x$ is getting multiplied by $-1.$ So if you increase $x$ by some number, the $y$-value decreases by that number.
In other words, each time you take one step to the right, you need to take one step down to stay on the line.
answered Aug 28, 2023 at 21:48