Two roads are represented by lines on a coordinate grid. two points on each of the roads are shown in the tables. (a) write the equation for road 1 in slope-intercept form. (b) write the equation for road 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 roads intersect, what are the coordinates of the point of intersection? use the substitution method and show your work.

(A) y - 7 = 2(x -2)

(B) y = -x + 6; y - 5 = -1(x + 1)

(C) Consistent independent

(D) (1, 5)

Step-by-step explanation:

(A) Road 1

(a) Slope

The point-slope formula for a straight line is

y₂ - y₁ = m(x₂ - x₁)     Insert the points  

 3 - 7 = m(0 - 2)

     -4 = m(-2)           Divide each side by -2

     m = -4/(-2)          Divide numerator and denominator by-2,

      m = 2

=====

(b) y-intercept

y₂ - y₁ = m(x₂ - x₁)

y₂ - 7 = 2(x₂ -2)

y - 7 = 2(x -2)

===============

(B) Road 2

(a) Slope

y = mx + b

Choose point (3,3)

m = (3 - 5)/(3 - 1)

m = -2/2

m = -1

=====

(b) y-intercept

y = mx +b

Choose point (3,3).

3 = -3 + b      Add 3 to each side

b = 6

=====

(c) Equation of line (point-slope form)

y = mx + b

y = -x + 6

=====

(d) Equation of line (slope-intercept form)

y - 5 = -1(x - 1)

===============

(C) Consistency

The two roads intersect.

There is only one point of intersection, so this is a consistent, independent system of equations

===============

(D) Point of intersection

(1)      y - 7 = 2(x -  2)

(2)          y =   -x + 6     Substitute (2) into (1)

-x + 6 – 7 = 2(x – 2)    Remove parentheses

       -x - 1 = 2x – 4      Add 4 to each side

       -x +3 = 2x            Add x to each side

             3 = 3x            Divide each side by 3

             x = 1               Substitute into 2

=====

            y = -1 + 6

           y = 5

The point of intersection is (1, 5).

see below

step-by-step explanation:

7.   there are 10 data points in the set.   the middle point is between 5 and 6.   the middle point in the top half is 8   and the middle point in the bottom half is 3. to find the iqr , take point 8 and subtract point 3

mid term   point 8 = 100   point 3 = 88

iqr = 100-88 = 12

final   point 8 = 93   point 3 = 78

iqr = 93 - 78 = 15

the final has the greatest iqr

6.   b - there is a high data value that causes the data set to be asymmetrical for the males: the data for males are high and asymmetrical .   there is an outlier for the males that skews the data

5.   the   iqr is a better measure of spread for the movies and basketball games.   since the basketball game has an outlier, we do not want to use standard deviation for measurement.  

3.   the exam median is much higher than the class median.   the median line is farther to the right on the exams

2.   there is no way to tell what the means are from the box and whisker plots.  

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225