Question

I need help who can salve for B, and C

If you can you are amazing! and you get points :)

Answer 1

A) the pairs are:

(2,7) and (0,3)

For the slope, we can use the equation:

s = (y2 - y1)/(x2 - x1)

so we have:

s=(7 - 3)/(2 - 0) = 2

so the linear equation has the form:

y = 2*x + b

now, we know that y = 7 when x= 2, so we can replace those values and find the value of b.

7 = 2*2 + b = 4 + b

b = 7 - 4 = 3

so the linear equation is: Y(x) = 2*x + 3

B) for the second set of data we have:

(1, 5) and (3,3)

the slope is:

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

then we have Y' = -1*x + b

replacing the values of the first pair we have:

5 = -1*1 + b

b = 5 + 1 = 6

then the equation is Y'(x) = -1*x + 6

c) the equations are:

Y(x) = 2*x + 3

Y'(x) = -1*x + 6

The signs of bot constants in the equations are different (in one the slope is negative and in the other positive) so it is easy to see that the equations are linear independent.

d) Lets see if the equations have a point in common:

for this, we can suppose Y' = Y for some value of x, then we have:

2*x + 3 = -1*x + 6

2x + 1x = 6 - 3

3x = 3

x = 3/3 = 1

now, we replace this value of x in one of the equations and find the value o y.

Y(1) = 2*1 + 3 = 5

then the point where the two lines intersect is the point (1, 5)

Answer 2

B(X+Y=6)

Explanation:

solution for question B:

Given ,two points in sidewalk2 are (1,5) and (3,3)

Equation of line in point slope form =
`y-y_(1) =m*(x-x_(1) )`

now the value of the slope
`m=(y_(2)-y_(1) )/(x_(2)-x_(1) )`

m=-1. therefore the equation of straight line in point-slope form will be y-5=-1(x-1).

Equation of line in slope intercept form is y=mx+c.

and slope we have already calculated above that is equal to -1.

hence equation of straight line in slope intercept form is y=-1(x)+6.

Solution for question C:

in a similar fashion calculate the equation of the straight line sidewalk1.

on solving both the equations(x+y=6 and 2x+y=11) we get a unique solution hence the system of equations is consistent.A given system of equations is said to be consistent if there exists a common point where all the lines intersect.