Question 158640This question is from textbook Algebra and Trigonometry Structure and Method book 2
: I have been working on this problem and I can't figure it out. I was wondering if someone could help me? Please and Thank you!! I deeply appreciate it!!
Find and equation in standard form of the line containing the given points.
(3/4,5/4),(-1/4,1/2)
This question is from textbook Algebra and Trigonometry Structure and Method book 2
Found 2 solutions by checkley77, gonzo:
Answer by checkley77(12844)   (Show Source):
You can put this solution on YOUR website! (3/4,5/4),(-1/4,1/2)
slope=(.5-1.25)/(-.25-.75)
slope=-.75/-1
slope=.75
.5=.75*-.25+b
.5=-.1875+b
b=.5+.1875
b=.61875
y=.75x+.61875
 (graph 300x200 pixels, x from -3 to 3, y from -3 to 3, .75x +.61875).
Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website! i would start by finding the equation in slope-intercept form.
general form of that equation is y = m*x + b
where m is the slope and b is the y-intercept when x = 0.
the slope is determined by (y2-y1)/(x2-x1)
y2 = 1/2
y1 = 5/4
x2 = -1/4
x1 = 3/4
y2-y1 = 1/2 - 5/4 = 2/4 - 5/4 = -3/4
x2-x1 = -1/4 - 3/4 = -4/4 = -1
slope becomes (-3/4) / -1 becomes 3/4
so part of the equation is y = (3/4)*x + b
to find b, we would use the formula to solve for one of the known coordinates.
using one of the given points of (3/4,5/4),
5/4 = 3/4*x + b becomes 5/4 = 3/4*(3/4) + b becomes 5/4 = 9/16 + b.
solving for b, the equation becomes b = 5/4 - 9/16 = 20/16 - 9/16 = 11/16.
looks like the b value is 11/16.
the slope intercept form of the equation then becomes y = 3/4*x + 11/16
to prove this is correct, take the same point and calculate the value of y given the value of x = 3/4.
we get y = (3/4)*(3/4) + 11/16 = 9/16 + 11/16 = 20/16.
the given value of y at that point is 5/4 which is the same as 20/16.
looks like the b value in the slope intercept formula is now correct.
calculating the value of y in the second set of coordinates given, we get
y = (3/4)*(-1/4) + 11/16
this becomes y = -3/16 + 11/16 = 8/16
the given y coordinate of 1/2 is the same as 8/16 so the formula looks good again.
now that we have the complete slope intercept form of the equation, we can translate to get the standard form of the equation.
the standard form of the equation is a*x + b*y = c
we start with the slope intercept form of the equation y = (3/4)*x + 11/16
we multiply both sides of the equation by 16 to remove the fractional parts.
the equation becomes 16*y = 12*x + 11
we subtract (12*x) from both sides of the equation to get 16*y - 12*x = 11
the standard form of the equation becomes -12*x + 16*y = 11
to prove this formula is correct we again take one of the points and see if the equation holds.
take (-1/4,1/2)
x = -1/4
y = 1/2
equation becomes -12*(-1/4) + 16*(1/2) = 11
this becomes 3 + 8 = 11
this becomes 11 = 11 proving the formula is correct.
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