Pls help, parallel lines equations

Question

Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the following equation

Point: (-1,-4)

Equation: 9x+3y=8

Answer 1

The general equation for a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. Let's start solving this problem by re-writing the equation of the line 9x + 3y = 8 in slope-intercept form:

1. subtract 9x from both sides of the equation to get 3y = -9x + 8
2. divide both sides of the equation by 3 to get y = (-9x + 8)/3
3. (-9x + 8)/3 can be written as (-9x÷3) + (8÷3),
4. which can be simplified to -3x + (8÷3)
5. The equation of the line in slope-intercept form is: y = -3x + (8÷3)

Let's remind ourselves what the question is asking us to do. We need to write the equation of a line (in slope-intercept form) that satisfies the following criteria:

1. The line is parallel to the line whose equation is y = -3x + (8÷3)
2. The line passes through the point (-1, -4)

The key to answering the question is this fact: Two lines must have the same slope in order to be parallel to each other. We now know that m = -3 for this line whose equation we are trying to figure out.

We also know that the point (-1, -4) lies on the line, so we can solve for b by plugging (x = -1) and (y = -4) into the equation:

-4 = (-3)(-1) + b

-4 = 3 + b

-7 = b

The equation of the line in slope-intercept form is

y = -3x - 7

Answer 2

Parallel lines have the same slope, so

m = -9/3 = -3

y = mx + b

y = -3x + b

-4 = -3(-1) + b

b = -7

y = -3x - 7

Test the answer.