Answer:
D
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
To calculate m use the slope formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (3, 6) and (x₂, y₂ ) = (8, 4)
m = = - , hence
y = - x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (8, 4), then
4 = - + c ⇒ c = 4 + =
y = - x + ← equation of line
9514 1404 393
Answer:
x-intercept: -14/9
y-intercept: 7
Step-by-step explanation:
This is one of the easiest forms for finding intercepts. To find the x-intercept, set y=0 and divide both sides by the coefficient of x.
-9x = 14 . . . . . set y=0
x = -14/9 . . . . divide by -9
__
To find the y-intercept, set x=0 and divide both sides by the coefficient of y.
2y = 14 . . . . set x=0
y = 7 . . . . . . divide by 2
The x-intercept is -14/9; the y-intercept is 7.
X²+y²-2y=7
using the formula that links Cartesian to Polar coordinates
x=rcosθ and y=r sin θ
substituting into our expression we get:
(r cos θ)²+(r sin θ)²-2rsinθ=7
expanding the brackets we obtain:
r²cos²θ+r²sin²θ=7+2rsinθ
r²(cos²θ+sin²θ)=7+2rsinθ
using trigonometric identity:
cos²θ+sin²θ=1
thus
r²=2rsinθ+7
Answer: r²=2rsinθ+7