What is an equation of the line that passes through the point (-5,-1)(−5,−1) and is parallel to the line 4x+5y=45

Answer 1

To start, let's break down the important information.

First, it says that the line is PARALLEL to the given equation. If two equations are parallel, that means they have the same slope. Slope is also known as "m" when an equation is written in Slope-Intercept Form: y=mx+b, where "m" is the slope. Next, we know that it passes through the point (-5,-1). This tells us that we can plug (substitute) -5 for x and -1 for y in the new equation.

Next, we need to change the given equation from Standard Form to Slope-Intercept Form so we can know the slope (since this is also the slope of our new equation because the lines are parallel).

1. 4x+5y=45 (Subtract 4x from both sides)
2. 5y= -4x+45 (Divide each term by 5)
3. y= -4/5x+9 (Equation is in Slope-Intercept Form)

Remember that "m" from y=mx+b is our slope. So, our slope of our equation is -4/5.

Now, we know that our new equation passes through the point (-5,-1) and has a slope of -4/5.

So, -1= -5(-4/5) + b (Simplify)

-1= 4 +b (Subtract 4 from both sides of equation)

b = -5

So, y= -4/5x -5 (Slope-Intercept Form).

I assume that they want the answer in Standard Form since that is the form of the equation given in the problem. In that case, you need to change your answer from Slope-Intercept Form to Standard Form.

So, starting with y= -4/5x -5 (Add -4/5x to both sides of the equation)

4/5x + y = -5 (Remember that you must have all whole numbers for an equation to be in Standard Form) So, multiply both sides of the equation by 5.

This gives you, 4x + 5y = -25 as your final answer.

I hope this helps!