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).

step-by-step explanation:

i think you should think about the question and not look online.

5x+40

5(x + 8)

7x - 49

7(x - 7)

18x + 9

9(2x + 1)

15x - 10

5(3x - 2)

step-by-step explanation:

for number one all you have to do is factor 5 out of 5x + 40

for number 2 factor 7 out of 7x - 49

for number three factor 9 out of 18x + 9

for number four factor 5 out of 15x - 10