Question

I NEED HELP just for (C) If you can get (C) for me you are amazing!

Answer 1

Answer:

Part 1) $y=2x+3$

Part 2) The equation in point slope form is equal to $y-5=-(x-1)$  and the equation in slope intercept form is equal to $y=-x+6$

Part 3) The system of equations is a consistent independent system

Part 4) The coordinates of the intersection point are x=1 and y=5

Step-by-step explanation:

Part 1) Write the equation of the sidewalks 1 in slope intercept form

we know that

The equation of the line in slope intercept form is equal to

$y=mx+b$

where

m is the slope

b is the y-intercept

we have the points

(2,7) and (0,3)

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{3-7}{0-2}$

$m=\frac{-4}{-2}=2$

The y-intercept is the point (0,3)

so

$b=3$

substitute

$y=2x+3$

Part 2) Write the equation of the sidewalks 2 in point slope form and then in slope intercept form

The equation in point slope form is equal to

$y-y1=m(x-x1)$

Find the slope

we have the points

(1,5) and (3,3)

substitute in the formula

$m=\frac{3-5}{3-1}$

$m=\frac{-2}{2}=-1$

take the point (1,5)

substitute

$y-5=(-1)(x-1)$

$y-5=-(x-1)$ ----> equation in point slope form

Convert to slope intercept form

Isolate the variable y

$y-5=-x+1$

Adds 5 both sides

$y=-x+1+5$

$y=-x+6$ ---> equation in slope intercept form

Part 3) Is the system of equations consistent independent, coincident or inconsistent

we have

$y=2x+3$ -----> equation A

$y=-x+6$ -----> equation B

Remember that the solution of the system is the intersection point both graphs

The slopes of the lines of the system are different, that means that the lines are not parallel, so the system has one solution (one intersection point)

Remember that

If a system has at least one solution, it is said to be consistent

If a consistent system has exactly one solution, it is independent

therefore

The system of equations is a consistent independent system

Part 4) Use the substitution method to solve the system

we have

$y=2x+3$ -----> equation A

$y=-x+6$ -----> equation B

substitute equation A in equation B

$2x+3=-x+6$

solve for x

Group terms

$2x+x=6-3$

$3x=3$

$x=1$

Find the value of y

substitute the value of x in equation A or equation B (is the same)

$y=2(1)+3=5$

The solution is the point (1,5)

therefore

The coordinates of the intersection point are x=1 and y=5