Write an equation in standard form of the line that passes through the given point and has the given slope m.
Can someone check my answers
(-2,6) m=1 -1x+y=8
(-7,8) m=-3 3x+y=-13
(9,-10)m=-4 4x+y=26
(-15,-4)m=1/2 -1/2x-y=23/2
the rest are ok
y= mx +b
-4 = (-15)(1/2) +b
-4 = -15/2 + b
-4+15/2 = b
7/2 = b
y = mx +b
y = x/2 +7/2
Ax + By = C
2(y) = 2(x/2 + 7/2)
2y = x + 7
-x +2y = 7
thanks
It is considered "poor form" to have the equation in standard form start with a negative x
or containing fractions.
so the 1st one I would write as
x - y = -8
the last one:
firs of all it should have been
(-1/2)x + y = 23/2
multiply each term by -2
x - 2y = -23
I assumed your constant would have been correct, wrong assumption.
go with kuai's solution, but write it as
x- 2y = -7
To write an equation in standard form of a line passing through a given point and having a given slope, we can use the point-slope form of a linear equation:
y - y₁ = m(x - x₁)
where (x₁, y₁) is the given point and m is the given slope.
Let's check your answers:
1) (-2, 6), m = 1
Using the point-slope form, we substitute the given values:
y - 6 = 1(x - (-2))
y - 6 = x + 2
Rearranging the equation to the standard form:
x - y = -4
2) (-7, 8), m = -3
Using the point-slope form, we substitute the given values:
y - 8 = -3(x - (-7))
y - 8 = -3x + 21
Rearranging the equation to the standard form:
3x + y = 29
3) (9, -10), m = -4
Using the point-slope form, we substitute the given values:
y - (-10) = -4(x - 9)
y + 10 = -4x + 36
Rearranging the equation to the standard form:
4x + y = 26
4) (-15, -4), m = 1/2
Using the point-slope form, we substitute the given values:
y - (-4) = 1/2(x - (-15))
y + 4 = 1/2x + 15/2
Rearranging the equation to the standard form:
1/2x - y = -23/2
So, it seems that your answers are incorrect for equations (1), (2), and (4). The correct standard form equations for these lines are:
1) (-2, 6), m = 1:
x - y = -4
2) (-7, 8), m = -3:
3x + y = 29
4) (-15, -4), m = 1/2:
1/2x - y = -23/2