Different texts use slightly different names for the form of the linear equation.
4x + 3y -12 = 0 -----> I would call general form
4x + 3y = 12 -------> standard form
y = (-4/3)x + 4 ---- > slope-y intercept form
point-slope form is a starting equation, usually ending up with one of the above.
Which ever method you use, finding the slope is a good start.
I will do the first one:
2 points (5,1) and (-3,4)
slope = (4-1)/(-3-5) = 3/-8 or -3/8
y-1 = (-3/8)(x-5) from y - y1 = m(x - x1)
at this point multiply each side by the denominator of the slope, if the slope is a fraction
8y - 8 = -3(x-5)
your fractions have disappeared, yeahhh!
8y - 8 = -3x + 15
3x + 8y = 23
at this stage I use the point that was not used and test if it satisfies my equation.
LS = 3(-3) + 8(4) = -9+32 = 23
RS = 23 , all is good!
Once you have the equation is the simple form of
3x + 8y = 23, you can go to any of the others
changing it to slope - y intercept form takes 2 steps
1. keep only the y term on the left side
3x + 8y = 23 -------> 8y = -3x + 23
2. divide each term by the coeffiecient of the y term
------> y = (-3/8)x) + 23/8
try the other two, let me know what you get
The point pairs chosen is (5, 1) and (-3, 4). First of all, the slope must be found out.
The formula for it is: slope = rise/run
slope = (4 - 1)/(-3 -5) = 3/-8 = -3/8
Point slope form: y - 1 = -3 (x - 5)/8
Slope intercept form: y - 1 = -3x/8 + 15/8
y = -3x/8 + 23/8
Standard form: 8y = -3x + 23
Thats all I rlly needed, thx~!
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