Ple

two sidewalks in a park are represented by lines on a coordinate grid. two points on each of the lines are shown in the tables.
sidewalk 1
x y
2 8
0 3
sidewalk 2
x y
1 4
3 3
(a) write the equation for sidewalk 1 in slope-intercept form.
(b) write the equation for sidewalk 2 in point-slope form and then in slope-intercept form.
(c) is the system of equations consistent independent, coincident, or inconsistent? explain.
(d) if the two sidewalks intersect, what are the coordinates of the point of intersection? use the substitution method and show your work.

  (a)  y = 5/2x +3

  (b)  y = -1/2x +9/2

  (c)  consistent, independent

  (d)  (0.5, 4.25)

Step-by-step explanation:

(a) The 2-point form of the equation of a line is a good place to start:

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

Filling in the point values, we have ...

  y = (8 -3)/(2 -0)(x -0) +3

  y = 5/2x +3 . . . . . . simplify

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(b) Similarly, filling in the point values, we have ...

  y = (3 -4)/(3 -1)(x -1) +4

  y = -1/2(x -1) +4 . . . . . . simplify

  y = -1/2x +9/2 . . . . . . . eliminate parentheses, collect terms

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(c) The lines have different slopes, so are consistent and independent.

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(d) Substituting for y, we have ...

  5/2x + 3 = -1/2x + 9/2

  5x +6 = -x +9 . . . . . . . . . . . . multiply by 2 to eliminate fractions

  6x = 3 . . . . . . . . . . . . . . . . . . add x-6

  x = 3/6 = 1/2 . . . . . . . . . . . . . divide by the x-coefficient

Using the equation for Sidewalk 2, we can find y:

  y = -1/2(1/2) +9/2

  y = 17/4

The point of intersection is (x, y) = (1/2, 17/4).

hey i’m new i won’t be answering any questions now bye peeps see you next time

the answer is; biodiversity resulting from few ancestors

adaptive radiation occurs when a population is subjected to a large natural environment with spatial ecological variations. the parts of the population in the different ecologies begin to adapt to their local environments. due to non-random mating across the large populations, this causes the different populations from the large population to speciate within their local environments. they, therefore, diverge to different species sharing a common ancestor.