Question 1030517
To graph using the slope and y-intercept,
you start by plotting the y-intercept point.
Then, using the slope, you find other points.
It works like this:
For {{{y=-x+3}}} ,
the slope is the {{{-1}}} that is the coefficient of {{{x}}} ,
and the y-intercept, is the {{{3}}} that appears as an independent term.
That y-intercept is the y coordinate for the point where the graph crosses the y-axis.
So you mark that point:
{{{drawing(300,300,-5,5,-2,8,
grid(1),blue(circle(0,3,0.1)),
blue(circle(0,3,0.15))
)}}}
From that point you move to the right and left using the slope.
A slope of {{{-1}}} means that as you move one grid square to the right (as {{{x}}} increases by {{{1}}} ),
{{{y}}} increases by {{{-1}}} (meaning that it decreases by {{{1}}} , and you move down one square.
So from point (0,3) you go to (1,2) , and from there to (2,1) , and to (3,0) ,
and to (4,-1), and so on.
Reversing movements you can go one square to the left and one up,\from (0,3) to (-1,4) , and then to (-2,5), and to (-3,6), and so on>
{{{drawing(300,300,-5,5,-2,8,
grid(1),blue(circle(0,3,0.1)),
blue(circle(0,3,0.15)),
blue(circle(1,2,0.1)),blue(circle(1,2,0.15)),
blue(circle(2,1,0.1)),blue(circle(2,1,0.15)),
blue(circle(3,0,0.1)),blue(circle(3,0,0.15)),
blue(circle(4,-1,0.1)),blue(circle(4,-1,0.15)),
blue(circle(-1,4,0.1)),blue(circle(-1,4,0.15)),
blue(circle(-2,5,0.1)),blue(circle(-2,5,0.15)),
blue(circle(-3,6,0.1)),blue(circle(-3,6,0.15)),
blue(line(-5,8,5,-2))
)}}} .
 
Note:
If the slope was {{{3/2}}} , when going from point to point,
you would move {{{2}}} spaces to the right and {{{3}}} up,
or reversing, you would move {{{2}}} spaces to the left and {{{3}}} down.