Please help me with this question

Mathematics

2 answers:

Mrrafil [7]2 years ago

4 0

Answers: Options A and D

Aleks04 [339]2 years ago

3 0

Answer:

A. The slope of m is -2/5

and

D. The slope of p is -5/2

Step-by-step explanation:

The slope is defined as the "change in y" over the "change in x" of a line. If you pick two points on a line --- (x1,y1) and (x2,y2) --- you can calculate the slope by dividing y2 - y1 over x2 - x1.

Line m goes through the points (-2,7) and (3,5). Slope = (y2 - y1)/(x2 - x1) = (5 - 7 )/(3 - -2) = -2/5

Line q goes through the points (6,15) and (0,0). Slope = (y2 - y1)/(x2 - x1) = (0 - 15 )/(0 - 6) = -15/-6 = 2.5 = 2 1/2 = 5/2

Line n goes through the points (-5,0) and (0,-2). Slope = (y2 - y1)/(x2 - x1) = (-2 - 0 )/(0 - -5) = -2/5

Line p goes through the points (6,15) and (10,5). Slope = (y2 - y1)/(x2 - x1) = (5 - 15 )/(10 - 6) = -10/4 = -2.5 = -2 1/2 = -5/2

Therfore the only true options are A and D

You might be interested in

The directrix of a parabola is y=−4y=−4 . The focus of the parabola is (−2,−2)(−2,−2) .

salantis [7]

Refer to the diagram shown below.

The directrix is y = -4 and the focus is (-2, -2).
Therefore the vertex is at (-2, -3).

Consider an arbitrary point (x,y) on the parabola.
The square of distance from the focus to the point is
(x+2)² + (y+2)²
The square of the distance from the point to the directrix is
(y+4)²

Therefore
(y+4)² = (y+2)² + (x+2)²
y² + 8y + 16 = y² + 4y + 4 + (x+2)²
4y = (x+2)² - 12
y = (1/4)(x+2)² - 3

Answer: $y = \frac{1}{4} (x+2)^{2} - 3$