Question 110458
what equation has a slope of 2 and a y-intercept of -5
solutions
<pre>
First let's draw it, starting with plotting the y-intercept
of b = 2

{{{drawing(400,375,-10,10,-10,10,
   
   locate(-.2,-4.55,X), locate(-.2,-4.55,O),
locate(-.2,-4.55,W), locate(-.2,-4.55,M),

   locate(-.27,-4.55,X), locate(-.27,-4.55,O),
locate(-.27,-4.55,W), locate(-.27,-4.55,M),

   locate(-.1,-4.55,X), locate(-.1,-4.55,O),
locate(-.1,-4.55,W), locate(-.1,-4.55,M),


   graph(400,375,-10,10,-10,10) )}}}

Now let's express the slope m = 2 as the fraction {{{2/1}}}

The numerator is the change in y, or +2.
The denominator is the change in x, or +1

From the y-intercept, we draw a line 2 units long UPWARD,
since +2 is positive.

   graph(400,375,-10,10,-10,10) )}}}

{{{drawing(400,375,-10,10,-10,10,
   
   locate(-.2,-4.55,X), locate(-.2,-4.55,O),
locate(-.2,-4.55,W), locate(-.2,-4.55,M),

   locate(-.27,-4.55,X), locate(-.27,-4.55,O),
locate(-.27,-4.55,W), locate(-.27,-4.55,M),

   locate(-.1,-4.55,X), locate(-.1,-4.55,O),
locate(-.1,-4.55,W), locate(-.1,-4.55,M),
line(-.1,-5,-.1,-3),line(.1,-5,.1,-3),

   graph(400,375,-10,10,-10,10) )}}}

Now from the end of that UPWARD line, we draw a line
+1 units RIGHTWARD, since +1 is positive.

{{{drawing(400,375,-10,10,-10,10,
   
   locate(-.2,-4.55,X), locate(-.2,-4.55,O),
locate(-.2,-4.55,W), locate(-.2,-4.55,M),

   locate(-.27,-4.55,X), locate(-.27,-4.55,O),
locate(-.27,-4.55,W), locate(-.27,-4.55,M),

   locate(-.1,-4.55,X), locate(-.1,-4.55,O),
locate(-.1,-4.55,W), locate(-.1,-4.55,M),
line(-.1,-5,-.1,-3),line(.1,-5,.1,-3),line(0,-3,1,-3),

   graph(400,375,-10,10,-10,10) )}}}

Now we draw a line through the y-intercept and the
end of the rightward line:

{{{drawing(400,375,-10,10,-10,10,
   
   locate(-.2,-4.55,X), locate(-.2,-4.55,O),
locate(-.2,-4.55,W), locate(-.2,-4.55,M),

   locate(-.27,-4.55,X), locate(-.27,-4.55,O),
locate(-.27,-4.55,W), locate(-.27,-4.55,M),

   locate(-.1,-4.55,X), locate(-.1,-4.55,O),
locate(-.1,-4.55,W), locate(-.1,-4.55,M),
line(-.1,-5,-.1,-3),line(.1,-5,.1,-3),line(0,-3,1,-3),

   graph(400,375,-10,10,-10,10,2x-5) )}}}

The equation of the line which has slope m and y-intercept b

is

y = mx + b

So:

The equation of the line which has slope 2 and y-intercept -5

is

y = (2)x + (-5)

or

y = 2x - 5.

Edwin</pre>