I got all of the questions on my homework except 4 this one, i need some help please.
Directons: True or False? determine whether the statement is true or false. and justify your answer.
*If the points (10, -3) and (2,-9) lie on the same line, then the point (-12, -37/2) also lies on that line.
So i need some help please, thanks in advance, 10POINTS 4 BEST ANSWER! :)
Directons: True or False? determine whether the statement is true or false. and justify your answer.
*If the points (10, -3) and (2,-9) lie on the same line, then the point (-12, -37/2) also lies on that line.
So i need some help please, thanks in advance, 10POINTS 4 BEST ANSWER! :)
-
Note: All numbers directly after a variable here should actually be subscripts.
Step 1: Find the slope
Slope = m = (y2 - y1)/(x2 - x1) = (-9 + 3)/(2 - 10) = (-6)/(-8) = 3/4
Step 2: Find the equation of the line using the point slope equation for a line
y - y1 = m(x - x1)
y + 3 = (3/4)*(x - 10)
y + 3 = (3/4)*x - 15/2
y = (3/4)*x - 21/2
Step 3: Plug in the x and y values for the point we want to test into our line and see if what we get returns true (if we get like 0 = 1, it's not true... If we get some statement that is true, it's true!)
y = (3/4)*x - 21/2
(-37/2) = (3/4)*(-12) - 21/2
(-37/2) = -9 - 21/2
-37/2 = -39/2
And, just to make it even more obvious, we can multiply both sides by -2...
37 = 39
Definitely false!
The point (-12, -37/2) doesn't lie on the line.
Hope this helps.
Step 1: Find the slope
Slope = m = (y2 - y1)/(x2 - x1) = (-9 + 3)/(2 - 10) = (-6)/(-8) = 3/4
Step 2: Find the equation of the line using the point slope equation for a line
y - y1 = m(x - x1)
y + 3 = (3/4)*(x - 10)
y + 3 = (3/4)*x - 15/2
y = (3/4)*x - 21/2
Step 3: Plug in the x and y values for the point we want to test into our line and see if what we get returns true (if we get like 0 = 1, it's not true... If we get some statement that is true, it's true!)
y = (3/4)*x - 21/2
(-37/2) = (3/4)*(-12) - 21/2
(-37/2) = -9 - 21/2
-37/2 = -39/2
And, just to make it even more obvious, we can multiply both sides by -2...
37 = 39
Definitely false!
The point (-12, -37/2) doesn't lie on the line.
Hope this helps.
-
start with the equation of the line. y=mx+b. first find m, the slope. (y1-y2)/(x1-x2) so (-3- -9)/(10-2) = 6/8 or 3/4. now we need to find the y intercept or b. now use either of the two points in your equation. lets use 10, -3 as our point and plug in those as x and y and solve for b. -3=(3/4)(10)+b. solving for b, b = -21/2. now to see if the point they give is on the line, lets plug in -12 for x and see what y is. if we get -37/2, the answer is true. otherwise, false.
y=(3/4)(-12)-(21/2). y = -9 - 21/2 or -39/2 so the answer is false.
y=(3/4)(-12)-(21/2). y = -9 - 21/2 or -39/2 so the answer is false.
-
The slope of the line is going to be the "y" distance between the points, divided by the "x" distance between the points.
So, the slope a = (-3+9)/(10-2) = 6/8 = 3/4
The line has an equation of y = ax+b
We know that a is 3/4, so -9 = (3/4)*2 + b, or that b is -10.5
So the equation of the line is y = (3/4)x + 21/10
Does this work with (-12, -37/2)?
(3/4)*(-12) - (10.5) = -39/2
NO, it's false.
So, the slope a = (-3+9)/(10-2) = 6/8 = 3/4
The line has an equation of y = ax+b
We know that a is 3/4, so -9 = (3/4)*2 + b, or that b is -10.5
So the equation of the line is y = (3/4)x + 21/10
Does this work with (-12, -37/2)?
(3/4)*(-12) - (10.5) = -39/2
NO, it's false.
-
Plug it into your graphing calculator on y= and look at the table. Boom.