Write the equation of the line that passes through the points (-7,0) and (-7, -8).
1 answer:
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Answer:
y = - 2x - 2
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 )
Calculate m using the slope formula
m =
with (x₁, y₁ = (- 2, 2) and (x₂, y₂ ) = (1, - 4)
m = =
= - 2, thus
y = - 2x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (- 2, 2), then
2 = 4 + c ⇒ c = 2 - 4 = - 2
y = - 2x - 2 ← equation of line
In this attached picture, we can prove that triangles AOB and COD are congruent. ∠CDO and ∠ABO are equal because they are alternate angles. Similarly, ∠OAB and ∠OCD are equal because they are alternate angles, as well. We have a rectangle and in the rectangle, opposite sides are equal; AB = CD. Then, because of Angle-SIde-Angle principle, we can say that triangles AOB and COD are equal. If triangles are congruent, then OD = OB and OC = AO. Applying congruency to the triangles ACD and BCD, we can see that these triangles are also congruent. It means that the diagonals are equal. Since, OD = OB and OC = AO, it proves that the point O simultaneously is the midpoint and intersection point for the diagonals.
