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# Consider the line y=-3X+5. Find the equation of a line that goes through (6,1) & is parallel to the line?

Solve:

If g(x)=-2x-7 find g(6)

Solve the system:

3x + 4y=1

y=x+2

### 3 Answers

- normanLv 71 decade agoFavorite Answer
1 = -3(6) + b

b = 19

y = -3x + 19

g(6) = -2(6) - 7 = -19

3x + 4(x+2) = 1

7x + 8 = 1

7x = -7

x = -1

y = -1 + 2 = 1

- 1 decade ago
i suppose u have 3 different qs

Q1) parallel lines imply that they have the same gradient.hence the line must have gradient= -3. now the general equation of a straight line is Y=MX+C. since you already know that M= -3, Y=-3X+C. Given further that it passes through (6,1), substitute x=6 and y=1 into the equation: 1=-3(6)+C

solving gives C=19. Hence your equation is y=-3X+19

Q2) g(6) means replacing all the x by 6. Hence, g(6)= -2(6)-7= -19

Q3) using substitution, 3x+4(x+2)=1

7x+8=1

x=-1

y= -1+2=1

hence the solution is (-1,1)

- Anonymous1 decade ago
Boy that sounds more like a command for me to do all of your homework for free, rather than a question!

Parallel lines have the same slope. You know that when a line is in the form of y = mx + b, that m is the slope. So we're looking for a line with the slope of -3 and includes the point (6,1). That gives us y = -3x + b. Plug in the point and solve for "b" to figure out what "b" is, and you can now write the full equation.

For the second problem, they give you the function, so just plug in x=6 to find the value of g(6).

For the third problem, go here to learn how to solve a system using substitution: