*Quick Linear equation - Equation of a line - Thanks

• nukeman
In summary, to determine an equation of a line through the points (-3,5) and (1,-3), you need to simplify the expression y - 5 = -2(x-(-3)) by dealing with the double negative first and then distributing the -2 to all terms. The final answer is y = -2x - 1. To isolate the y term, you add 5 to both sides of the equation.
nukeman

Homework Statement

Determine an equation of a line through -3,5 and 1, -3

so... What i got is

y - 5 = -2(x-(-3) )

So that turns into

y - 5 = -2x + 3 correct?

now i am suppose to simplify, and the answer is

y = -2x -1

how did they get y = -2x -1 from y - 5 =-2x + 3

?? Can anyone please explain the steps they did to get that final answer?

The Attempt at a Solution

y - 5 = -2(x-(-3) ) Does NOT turn into y - 5 = -2x + 3?

Deal with the double negative first, then distribute the -2 to ALL terms it’s multiplied by, so:

y - 5 = -2(x-(-3) ) -> y - 5 = -2(x+3) -> y - 5 = -2x-6 -> y= -2x-1

wow, thanks. That makes much more sense!

ok so y - 5 = -2x-6

now you to get rid of the y - 5, you ad 5 to both sides correct?

y= -2x-1

JonF said:
y - 5 = -2(x-(-3) ) Does NOT turn into y - 5 = -2x + 3?

Deal with the double negative first, then distribute the -2 to ALL terms it’s multiplied by, so:

y - 5 = -2(x-(-3) ) -> y - 5 = -2(x+3) -> y - 5 = -2x-6 -> y= -2x-1

nukeman said:
wow, thanks. That makes much more sense!

ok so y - 5 = -2x-6

now you to get rid of the y - 5, you ad 5 to both sides correct?
You're not getting rid of y - 5 - you're just isolating y to get it all by itself. Yes, you add 5 to both sides.
nukeman said:
y= -2x-1

1. What is a quick linear equation?

A quick linear equation is a mathematical expression that represents a straight line on a graph. It is typically written in the form y = mx + b, where m is the slope of the line and b is the y-intercept.

2. How do you find the equation of a line?

To find the equation of a line, you need to know the slope (m) and y-intercept (b) of the line. You can then plug these values into the equation y = mx + b to get the equation of the line.

3. What is the importance of knowing the equation of a line?

Knowing the equation of a line allows you to easily plot the line on a graph and make predictions about the relationship between the x and y values. It also helps in solving real-world problems and understanding the behavior of linear systems.

4. How does the slope affect the equation of a line?

The slope (m) is a measure of how steep or flat a line is. It determines the rate of change between the x and y values. A larger slope means a steeper line, while a smaller slope means a flatter line. The slope also determines the direction of the line - a positive slope goes up from left to right, while a negative slope goes down from left to right.

5. Can you have a horizontal or vertical line as the equation of a line?

Yes, you can have a horizontal or vertical line as the equation of a line. A horizontal line has a slope of 0 and its equation would be y = b, where b is the y-intercept. A vertical line has an undefined slope and its equation would be x = a, where a is the x-intercept.

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