Write an equation in standard form of the line that passes through the given points.
Can someone check my answers?
(2,6)(3,8) -2x+y=2
(7,-3)(4,-1) 4/3x+y=19/3
(3,-8)(5,-9) 1/2x+y=-13/2
(-5,6)(2,-3) 9/7x+y=-3/7
(-3,-1)(6,-8) 7/9x+y=-10/3
better form ....
-2x + y = 2 ---> 2x - y = -2
4/3x+y=19/3 ----> 4x + 3y = 19
1/2x+y=-13/2 ----> x + 2y = -13
9/7x+y=-3/7 ---->9x + 7y = -3
7/9x+y=-10/3 ----> 7x + 9y =-30
can you see what I did?
A proper way to write equation in standard form:
- no fractions should show up (You can always get rid of fractions by multiplying each term by the LCD)
- the x term should be first and be positive
Now to check if they are right, simply sub in your points, both must satisfy your equation.
I think the second one is wrong!
slope = (-1+3)/(4-7) = - 2/3
using (4,-1)
y+1 = (-2/3)(x-4)
3y + 3 = -2x + 8
2x + 3y = 5
........ both points work in this one
-2x + y = 2
2x + 3y = 5
x + 2y = -13
9x +7y = -3
7x + 9y = -30
thanks
To find the equation of a line in standard form given two points, you can use the slope-intercept form and convert it into standard form.
Here's how to check your answers and convert them into standard form:
1. (2,6)(3,8)
First, calculate the slope of the line using the formula: slope (m) = (y2 - y1) / (x2 - x1)
m = (8 - 6) / (3 - 2) = 2/1 = 2
Using the point-slope form: y - y1 = m(x - x1), plug in one of the given points (2,6):
y - 6 = 2(x - 2)
y - 6 = 2x - 4
y = 2x + 2
Now, convert the equation into standard form: -2x + y = 2
2. (7,-3)(4,-1)
Similarly, calculate the slope using the formula: m = (-1 - (-3)) / (4 - 7) = 2/3
Using the point-slope form: y - y1 = m(x - x1), plug in one of the given points (7,-3):
y - (-3) = (2/3)(x - 7)
y + 3 = (2/3)x - 14/3
y = (2/3)x - 14/3 - 3
y = (2/3)x - 14/3 - 9/3
y = (2/3)x - 23/3
Now, convert the equation into standard form: -2x + 3y = -23
3. (3,-8)(5,-9)
Using the formula for slope: m = (-9 - (-8)) / (5 - 3) = -1/2
Using the point-slope form: y - y1 = m(x - x1), plug in one of the given points (3,-8):
y - (-8) = (-1/2)(x - 3)
y + 8 = (-1/2)x + 3/2
y = (-1/2)x + (3/2) - 8
y = (-1/2)x + (3/2) - 16/2
y = (-1/2)x - 13/2
Now, convert the equation into standard form: (1/2)x + y = -13/2
4. (-5,6)(2,-3)
Calculate the slope using the formula: m = (-3 - 6) / (2 - (-5)) = -9/7
Using the point-slope form: y - y1 = m(x - x1), plug in one of the given points (-5,6):
y - 6 = (-9/7)(x - (-5))
y - 6 = (-9/7)(x + 5)
y - 6 = (-9/7)x - 45/7
y = (-9/7)x - 45/7 + 42/7
y = (-9/7)x - 3/7
Now, convert the equation into standard form: (9/7)x + y = -3/7
5. (-3,-1)(6,-8)
Calculate the slope using the formula: m = (-8 - (-1)) / (6 - (-3)) = -7/9
Using the point-slope form: y - y1 = m(x - x1), plug in one of the given points (-3,-1):
y - (-1) = (-7/9)(x - (-3))
y + 1 = (-7/9)(x + 3)
y + 1 = (-7/9)x - 21/9
y = (-7/9)x - 21/9 - 9/9
y = (-7/9)x - 30/9
Now, convert the equation into standard form: (7/9)x + y = -10/3
Please note that the standard form of a linear equation is in the form Ax + By = C, where A, B, and C are constants.