MATH SOLVE

1 month ago

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

Accepted Solution

A:

Answer:Part 1) [tex]y=2x+3[/tex]Part 2) The equation in point slope form is equal to [tex]y-5=-(x-1)[/tex] and the equation in slope intercept form is equal to [tex]y=-x+6[/tex]Part 3) The system of equations is a consistent independent systemPart 4) The coordinates of the intersection point are x=1 and y=5Step-by-step explanation:Part 1) Write the equation of the sidewalks 1 in slope intercept formwe know thatThe equation of the line in slope intercept form is equal to[tex]y=mx+b[/tex]wherem is the slopeb is the y-interceptwe have the points(2,7) and (0,3)Find the slopeThe formula to calculate the slope between two points is equal to[tex]m=\frac{y2-y1}{x2-x1}[/tex]substitute the values[tex]m=\frac{3-7}{0-2}[/tex][tex]m=\frac{-4}{-2}=2[/tex]The y-intercept is the point (0,3)so[tex]b=3[/tex]substitute[tex]y=2x+3[/tex]Part 2) Write the equation of the sidewalks 2 in point slope form and then in slope intercept formThe equation in point slope form is equal to[tex]y-y1=m(x-x1)[/tex]Find the slopewe have the points(1,5) and (3,3)substitute in the formula[tex]m=\frac{3-5}{3-1}[/tex][tex]m=\frac{-2}{2}=-1[/tex]take the point (1,5)substitute[tex]y-5=(-1)(x-1)[/tex][tex]y-5=-(x-1)[/tex] ----> equation in point slope formConvert to slope intercept formIsolate the variable y[tex]y-5=-x+1[/tex]Adds 5 both sides[tex]y=-x+1+5[/tex][tex]y=-x+6[/tex] ---> equation in slope intercept formPart 3) Is the system of equations consistent independent, coincident or inconsistentwe have[tex]y=2x+3[/tex] -----> equation A[tex]y=-x+6[/tex] -----> equation BRemember that the solution of the system is the intersection point both graphsThe 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 thatIf a system has at least one solution, it is said to be consistentIf a consistent system has exactly one solution, it is independentthereforeThe system of equations is a consistent independent systemPart 4) Use the substitution method to solve the systemwe have[tex]y=2x+3[/tex] -----> equation A[tex]y=-x+6[/tex] -----> equation Bsubstitute equation A in equation B[tex]2x+3=-x+6[/tex]solve for xGroup terms[tex]2x+x=6-3[/tex][tex]3x=3[/tex][tex]x=1[/tex]Find the value of ysubstitute the value of x in equation A or equation B (is the same)[tex]y=2(1)+3=5[/tex]The solution is the point (1,5)thereforeThe coordinates of the intersection point are x=1 and y=5