The answer is B. 12
2 answers:
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Answer:
Part A) The slope is
Part B) The equation of the line is
Step-by-step explanation:
Part A) What is the slope of the graph?
we know that
The formula to calculate the slope between two points is equal to
Looking at the graph it takes any two points
(-2,0) and (0,-1)
substitute the values in the formula
Part B) Write an equation for the line
we know that
The equation of the line in slope intercept form is
where
m is the slope
b is the y-coordinate of the y-intercept
we have
----> the y-intercept is the point (0,-1)
substitute
Answer:
(0, 4) and (- 4, 0)
Step-by-step explanation:
We require the equation of the circle
The equation of a circle centred at the origin is
x² + y² = r² ( r is the radius )
The radius is the distance from the centre to a point on the circle
To calculate r use the distance formula
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (, - 2)
r =
= =
= 4, hence
x² + y² = 16 ← equation of circle
given y - x = 4 ⇒ y = x + 4
Substitute y = x + 4 into the equation of the circle
x² + (x + 4)² = 16 → distribute and simplify left side
x² + x² + 8x + 16 = 16
2x² + 8x + 16 = 16 ( subtract 16 from both sides )
2x² + 8x = 0
2x(x + 4) = 0
Equate each factor to zero and solve for x
2x = 0 ⇒ x = 0
x + 4 = 0 ⇒ x = - 4
Substitute these values into y = x + 4 for corresponding y- coordinates
x = 0 : y = 4 ⇒ (0, 4)
x = - 4 : y = - 4 + 4 = 0 ⇒ (- 4, 0)
The points of intersection are (0, 4) and (- 4, 0)