Ineed who can salve for b, and c

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

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)

the answers c