|
Question 1194392: Find the intercepts and sketch the graph of each line:
1. x + 2y = 2
2. 3x - y = 6
3. 4x - y = 2
4. -2x + y = 3
5. 2x + y = 1
6. 3x - 4y = -12
Given a point and the slope, graph the line and find the equation:
7. (3,1) m = 1/2
8. (-1,-1) m = -2
9. (4,-1) m = -2/3 (negative two over three)
10. (0,0) m = -4/3 (negative four over three)
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52754)   (Show Source):
You can put this solution on YOUR website! .
Don't you want, in addition, the tutors would solve all problems from your textbook, one after other ?
And then from your next textbook, for the next year ?
And the year after next ?
//////////////
Too many questions for one post.
See the rules of posting to this forum in this page
https://www.algebra.com/tutors/students/ask.mpl?action=ask_question&topic=Equations&return_url=http://www.algebra.com/algebra/homework/equations/
from which you post your problems.
It is assumed that you read these rules before posting.
It is also assumed that you do understand what is written there and follow the rules.
Those who violate them, work against their own interests.
Answer by math_tutor2020(3816)  (Show Source):
You can put this solution on YOUR website!
I'll show how to solve problems 1, 2, 7 and 8 as four examples to get you started.
============================================================
Problem 1
To find the x intercept, plug in y = 0 and solve for x.
x+2y = 2
x+2(0) = 2
x = 2
The x intercept is 2, meaning it crosses the horizontal x axis at 2.
Plug in x = 0 and solve for y to get the y intercept.
x+2y = 2
0+2y = 2
2y = 2
y = 2/2
y = 1
The y intercept is 1.
This is where the graph crosses the vertical y axis.
To graph this line, plot the x and y intercepts mentioned. Then draw a straight line through those two points.
============================================================
Problem 2
We follow the same idea as problem 1.
Let's find the x intercept
3x - y = 6
3x - 0 = 6
3x = 6
x = 6/3
x = 2
Now the y intercept
3x - y = 6
3(0) - y = 6
0 - y = 6
-y = 6
y = 6/(-1)
y = -6
The x and y intercepts are 2 and -6 in that order.
Meaning that this line goes through the points (2,0) and (0,-6).
Repeat these ideas for problems 3 through 6.
============================================================
Problem 7
Start with the point (3,1)
Now move 1 unit up and 2 units to the right to arrive at (5,2). This motion of "1 unit up, 2 units right" is directly from the slope 1/2.
Then draw a straight line through (3,1) and (5,2) to complete the graph.
Slope = rise/run = 1/2
rise = 1 = go 1 unit up
run = 2 = go 2 units right
Now let's find the y intercept based on this point and slope
The point (x1,y1) = (3,1) is on the line
m = 1/2 is the slope
Use the aptly named point-slope form to isolate y
y - y1 = m(x - x1)
y - 1 = (1/2)(x - 3)
y - 1 = (1/2)x + (1/2)*(-3)
y - 1 = (1/2)x - 3/2
y = (1/2)x - 3/2 + 1
y = (1/2)x - 3/2 + 2/2
y = (1/2)x + (-3+2)/2
y = (1/2)x - 1/2
The equation is in the format y = mx+b
m = 1/2 = slope
b = -1/2 = y intercept
============================================================
Problem 8
We'll use the same idea as problem 7.
Let's find the equation first.
y - y1 = m(x - x1)
y - (-1) = -2(x - (-1))
y + 1 = -2(x + 1)
y + 1 = -2x - 2
y = -2x - 2-1
y = -2x - 3
Now it is in y = mx+b form
m = -2 = slope
b = -3 = y intercept
To find another point on this line, start at the given point (-1,-1)
Then move 2 units down and 1 unit to the right to arrive at (0, -3)
This "2 unit down, 1 unit right" motion is because of the slope
slope = -2 = -2/1 = rise/run
rise = -2 = go 2 units down
run = 1 = go 1 unit right.
The graph of this equation is a straight line that goes through (-1,-1) and (0,-3)
The same ideas apply for problems 9 and 10.
|
|
|
| |
