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 7
0 3
sidewalk 2
x y
1 5
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.

where's the diagrams?

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}