Question

Using complete sentences, explain how to find the equation of the line, in standard form and slope–intercept form, passing through (–1, –7) and (1, –1). Also compare the benefits of writing an equation in standard form to the benefits of writing an equation in slope–intercept form.

Answer 1

the eq of the line is y=3x-4

you're given 2 points on a line, (-1,-7) and (1,-1)
you can easily plug in the first one into the slope-intercept formula

y = mx+b
-7=m(-1) + b
-7=-m +b this is the Slope-Intercept form
or you can change it to Standard Form...
-m+b=-7 get rid of the - m
(-1)(-m)+b=-7 (-1)
m-b=7 first equation of the system

using the 2d point (1,-1) will get the 2d eq of the system
again, beginning with the Slope-intercept formula--
y = mx+b
-1 = m (1) + b
-1 = m + b this is the Slope-intercept form
or
m + b = -1 back to Standard form.....second equztion of the system

now we have a system of equations:
m - b = 7 and
m + b = -1

Using the Ellimination method, we get rid of b and m = 3
m-b=7
m+b=-1
----------
2m = 6
m = 3 this the slope

now we need to find b

using the first eq m - b = 7
3 - b = 7
3 -3 -b = 7 -3
-b = 4
b=4 this is the y intercept

you can now put it all together into the equation for the system y=3x-4


The different equation forms lend themselves to different methods of solving equations for the unknowns. The Standard form allows you to use the Ellimination method easily or the Substitution method. The Slope-Intersept form lends itself to graphing the equation/line easiler than the Standard form.