SOLUTION: Good Sunday Morning! I am trying to find the slope-intercept form of the equation of the line through the point (-1, 2), parallel to the line -4x- 9y = -7. Thanks for the hel

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Question 380971: Good Sunday Morning!
I am trying to find the slope-intercept form of the equation of the line through the point (-1, 2), parallel to the line -4x- 9y = -7.
Thanks for the help!
Denise
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
If the line is parallel then it has the same slope.

The line it is parallel to is the line given by the equation -4x - 9y = -7

convert that line to the slope intercept form by solving for y.

you will get y = (-4/9)*x + (7/9)

The slope of that line is equal to (-4/9)

That will be the slope of your new line.

The general equation for the slope intercept form is y = mx + b where m is the slope and b is the y intercept.

Since you have the slope, the general form becomes y = (-4/9)*x + b

To find the y intercept, you substitute the point values that the line passes through.

The point values that you have that the line passes through are (-1,2).

That means that x = -1 and y = 2.

Substitute in the equation of y = (-4/9)*x + b to get:

2 = (-4/9)*(-1) * b

Simplify to get:

2 = (4/9) * b

Solve for b to get:

b = 2 - (4/9) = (18/9) - (4/9) = (14/9)

The equation of your parallel line should be:

y = (-4/9)*x + (14/9)

graph both equations and you will see that they are parallel.

To prove that the slope intercept form of your original equation is good, you need to substitute the (x,y) values derived from the slope intercept form of the equation and see if the original equation is true.
Your original equation is -4x-9y=-7.

The slope intercept form of this equation is y = (-4/9)*x + (7/9)

If we let x = 18, then y = (-4/9)*18 + (7/9) = -7.22222222

If we let x = 18 and y = -7.22222222, then -4x - 9y = -7 becomes -72 + 65 = -7

the translation from the standard form of the equation (-4x-9y=-7) to the slope intercept form of the equation ( y = (-4/9)*x + (7/9)) is good.

The line parallel to it is therefore good because we calculated that correctly based on the slope intercept form of the original equation.