Question 821734
---
I will do two of the more difficult ones for you, and you can do the rest: 
---
first, you want to make sure the equation is in standard linear equation form, which is this:
ax + by = c
---
generally, a, b, and c may be positive, negative, or zero.
---
EQUATION 1:
---
in this case, we need to simplify:
3(x + 4y) = -24
---
3x + 12y = -24
---
and presto, it's now in standard linear equation form, with a=3, b=12, and c=-24
---
to solve the linear equation, copy and paste this:
3 12 -24
into the "Standard form: A B C" input box here: https://sooeet.com/math/linear-equation-solver.php
---
answer:
x-intercept = -8
y-intercept = -2
slope = -0.25
---
now that we have the above information, we can put the equation in slope-intercept form: y = mx + b
where:
m = slope
b = y-intercept
NOTE: this b (y-intercept) is not the same as the b above (from the standard linear equation form)
---
so we have this now:
y = (-0.25)x + (-2)
y = -0.25x - 2
---
graph:
---
{{{ graph( 300, 300, -10, 2, -4, 2, -0.25x - 2) }}}
---
---
---
EQUATION 2:
---
y = -3x + 12
---
this one is already in slope-intercept form: y = mx + b
where:
m = slope = -3
b = y-intercept = 12
---
to find the x-intercept just set y=0 and solve for x, like so:
y = -3x + 12
0 = -3x + 12
3x = 12
x = 4
x-intercept = 4
---
now to graphing:
---
graph:
---
{{{ graph( 300, 300, -2, 5, -2, 14, -3x + 12) }}}
---
---
---
as for the remaining equations, they are all solved by one or the other of the above methods.
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php