Determining the equation of a line

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In summary, for part a, the equation of the line is y= 1/2x -3 and for part b, the equation of the line is y=5x -2.
  • #1
Kirito123
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Question:
Determine the equation of a line for the following:
a) The line that has an x-intercept of 6 and that passes through the point (2, –2)
b)The line that never intersects 5xy + 3 = 0, and which is five grid squares lower than that line

Relevant equation:
y= mx+b

Attempt at a solution:
for a, I know that the x intercept is +6, and the line has to pass through the points (2, -2). Does this mean i have to graph the line first, then solve for the slope of the line (m) and use any point on the line (x,y) to solve for b once i solve for the slope:

After graphing the line i found the slope 2/4 or 1/2. I had to find b so i put the values i got in standard form:
2=1/2(-2) + b
I simplified both sides of the equation.
2=1/2(−2)+b
Simplify: 2=b−1
I then flip the equation.
b−1=2
I added 1 to both sides.
b−1+1=2+1
b=3
My answer:
b=3Is that the correct way to do it??for b, i solved for the slope intercept form of the line, then i graphed it, and counted five grid squares down. Then, i calculated the slope and y-intercept of the new line:

5xy + 3 = 0
5xy = -3
y = -5x -3
y = -5x -3 /-1
y = 5x + 3

after graphing this line, i counted 5 square grids down and got new line that has a y-intercept of -2, and the same slope as the original line (+5)
so the equation of the line for part b is:
y=5x -2

is this correct?
 
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  • #2
Kirito123 said:
Question:
Determine the equation of a line for the following:
a) The line that has an x-intercept of 6 and that passes through the point (2, –2)
b)The line that never intersects 5xy + 3 = 0, and which is five grid squares lower than that line

Relevant equation:
y= mx+b

Attempt at a solution:
for a, I know that the x intercept is +6, and the line has to pass through the points (2, -2). Does this mean i have to graph the line first, then solve for the slope of the line (m) and use any point on the line (x,y) to solve for b once i solve for the slope:

After graphing the line i found the slope 2/4 or 1/2. I had to find b so i put the values i got in standard form:
2=1/2(-2) + b
I simplified both sides of the equation.
2=1/2(−2)+b
Simplify: 2=b−1
I then flip the equation.
b−1=2
I added 1 to both sides.
b−1+1=2+1
b=3
My answer:
b=3Is that the correct way to do it??for b, i solved for the slope intercept form of the line, then i graphed it, and counted five grid squares down. Then, i calculated the slope and y-intercept of the new line:

5xy + 3 = 0
5xy = -3
y = -5x -3
y = -5x -3 /-1
y = 5x + 3

after graphing this line, i counted 5 square grids down and got new line that has a y-intercept of -2, and the same slope as the original line (+5)
so the equation of the line for part b is:
y=5x -2

is this correct?
Part b is correct.

Part a is not. You plugged in x and y incorrectly.
 
  • #3
B looks right, both lines have the same slope which means they are parallel and so will never intersect.

For A, you can check your solution as you have two points that must be on the line (2,-2) and the x-intercept point. Do you know the coordinates of the x-intercept?
 
  • #4
is this the answer for part a?
-2 = 2/4(2) +b
-2 = 1 + b
-3 = b

so the equation of the line for part a is:
y= 1/2x -3
is this correct??
 
  • #5
Kirito123 said:
is this the answer for part a?
-2 = 2/4(2) +b
-2 = 1 + b
-3 = b

so the equation of the line for part a is:
y= 1/2x -3
is this correct??

Take the two points mentioned earlier and plug them back into the equation. This is how you check you answer. So plug in the X intercept point which you should kno it's coordinates since it's an intercept point on the X axis. Similarly for the other point if either fail then you know your solution is wrong and so it's time to review your steps.

We can't do your homework for you.
 
  • #6
so i plugged the x-intercept point into my equation, and here's what i got:
(6,0)

0 = 1/2(6) -3
0 = 3-3
0 = 0
so because both sides of the equation are balanced, I am assuming my equation is correct?
 
  • #7
Ok and when you plug in 2,-2 what do you get?

If that balances too then you have demonstrated that your solution is correct.
 
  • #8
-2 = 1/2(2) -3
-2 = 1 - 3
-2 = -2

It does balance, so I'm guessing that my solution is correct?
 
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  • #9
As a post analysis of your problem review your original steps to understand where you went wrong. Many times students will commit the same mistakes over and over losing valuable points on an exam.

My brother would do something similar, he'd solve the problem but make a mistake in the check math and go back to "fix" his answer. Once he saw what he was doing he spent more time checking his check too.
 
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  • #11
Thanks for the advice and the help!
 
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Related to Determining the equation of a line

What is the equation of a line?

The equation of a line is a mathematical representation of a straight line on a graph. It can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept.

How do you determine the slope of a line?

The slope of a line is the measure of how steep the line is. It can be calculated by finding the change in y-values over the change in x-values between any two points on the line. This can be represented by the formula (y2 - y1) / (x2 - x1).

What is the y-intercept of a line?

The y-intercept of a line is the point where the line crosses the y-axis on a graph. It is represented by the value b in the equation y = mx + b. It can also be determined by finding the value of y when x is equal to 0.

How do you find the equation of a line from two points?

To find the equation of a line from two points, you can use the slope formula (y2 - y1) / (x2 - x1) to find the slope. Then, plug in one of the points and the slope into the point-slope form of a line, y - y1 = m(x - x1). Finally, rearrange the equation to get it in the standard form y = mx + b.

What is the difference between a positive and a negative slope?

A positive slope indicates that the line is increasing as you move from left to right on the graph, while a negative slope indicates that the line is decreasing. In terms of the equation, a positive slope has a positive value for m, while a negative slope has a negative value for m.

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