Find the slope a and y of a line 4x+8
- Thread starter Rabinov23
- Start date
Well, if you're ever unsure of an answer(s), you can always check them yourself. There's two main ways I can think of to do this. One is quick and straightforward; the other's more involved but will hopefully lead to a greater understanding of the principles. I'll start with the "hard" way first - review the definitions of y-intercept and slope.
The y-intercept of a line is the value of \(y\) at the point where the line crosses the y-axis. Think about what you know about graphing. Where is the y-axis? What is the x-coordinate of any point on the y-axis? What happens when you plug this x-value into the equation? Do you get 4? If not, what do you get?
The slope of a line is defined as rise over run, or it may also be expressed as \(\displaystyle \frac{\text{change in y}}{\text{change in x}}\). Your proposed answer, that the slope is \(\displaystyle 2 = \frac{2}{1}\), would mean that for every 1 unit that \(x\) increases, \(y\) increases by 2 units (or if \(x\) decreases by 1 unit, then \(y\) decreases by 2 units). Let's see if this is true. If we plug \(x = 1\) into the equation, we find that \(y = 4(1) + 8 = 12\). If your slope is correct, we should see that the equation \((12 + 2) = 4(1 + 1) + 8\) holds true. Does it? If it doesn't hold true, what do you suppose the slope should be in order to make it a true equation?
Next, we can look at the "easy" way which doesn't necessarily confer any understanding of the ideas. You've got the line in \(y = mx + b\) form already. So what does \(m\) represent in this equation? And what is your \(m\)? What does \(b\) represent in this equation? And what is your \(b\)?
The y-intercept of a line is the value of \(y\) at the point where the line crosses the y-axis. Think about what you know about graphing. Where is the y-axis? What is the x-coordinate of any point on the y-axis? What happens when you plug this x-value into the equation? Do you get 4? If not, what do you get?
The slope of a line is defined as rise over run, or it may also be expressed as \(\displaystyle \frac{\text{change in y}}{\text{change in x}}\). Your proposed answer, that the slope is \(\displaystyle 2 = \frac{2}{1}\), would mean that for every 1 unit that \(x\) increases, \(y\) increases by 2 units (or if \(x\) decreases by 1 unit, then \(y\) decreases by 2 units). Let's see if this is true. If we plug \(x = 1\) into the equation, we find that \(y = 4(1) + 8 = 12\). If your slope is correct, we should see that the equation \((12 + 2) = 4(1 + 1) + 8\) holds true. Does it? If it doesn't hold true, what do you suppose the slope should be in order to make it a true equation?
Next, we can look at the "easy" way which doesn't necessarily confer any understanding of the ideas. You've got the line in \(y = mx + b\) form already. So what does \(m\) represent in this equation? And what is your \(m\)? What does \(b\) represent in this equation? And what is your \(b\)?
D
Deleted member 4993
Guest
In your subject-line you said:
of a line 4x+8
equation of that line is:
y = 4x + 8
and not what you wrote above (y=2x+4)
Thus your slope and intercept calculation above is incorrect.
Is he just trying to solve the x and y-intercept?
D
Deleted member 4993
Guest
Correct