Question

2. Two sidewalks in a park are represented by lines on a coordinate grid. Two points on each of the lines are shown inthe tablestable 1 (sidewalk 1)x y2 50 1table 2 (sidewalk 2)1 33 -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 convert to slope-intercept form.(c) Is the system of equations consistent independent, coincident, or inconsistent? Explain.(d) Use the substitution or elimination method to solve your system, and explain which one you picked. If the two sidewalks intersect, what are the coordinates of the point of intersection?

Answer 1

a) slope-intercept form: y = 2x + 1

b) point slope form: y - 3 = -3(x - 1)

Step-by-step explanation:

Slope formula:

`m\text{ = }(y_2-y_1)/(x_2-x_1)`

a) sidewalk 1 (table 1)

slope = (1-5)/(0-2) = -4/-2

slope = 2

equation of sidewalk 1 in slope-intercept form: y = mx + c

where m = slope, c = intercept

we need to find the intercept using any point: (2, 5) = (x, y)

5 = 2(2) + c

c = 1

slope-intercept form: y = 2x + 1

b) sidewalk 2(table 2)

slope = (-3-3)/(3-1) = -6/2

slope = -3

`poi\text{ nt slope: }y-y_1=m(x-x_1)`

using any point: (1, 3) = (x, y)

point slope form: y - 3 = -3(x - 1)