What is the slope of the line 5x + 2y = 10?

Question

1.A relation where every x-value produces a unique y-value is called a ___________.

2. Write the equation of the line given the slope and the y-intercept m = 5, y-intercept (0, -3)

3. Write the equation of the line given the slope and a point on the line m = 3, point (5, 10)

4. What is the slope of the line 5x + 2y = 10?

5. Change the given equation into slope-intercept form. 2x + 5y = -10

6. What is the slope of the line for the equation x = 5?

7. Which is the best description of the graph of the inequality y > 2x – 3?

8. Identify the x and y intercepts for the equation 4x – 3y = 12.

9. What is the value of f(5) for the function f(x) = 3x - 4

10. What is the slope of the line through the points (2, 0) and (0, 8)? m = _?_

11. What is the slope of the line through the points (2, 0) and (0, 8)? m = _?_

12. What is the value of g[f(4)] for the functions f(x) = 2x + 1 and g(x) = 2x - 5?

Answer 1

Wow lots of questions. Here we go:

For the question in your title, write in slope - y intercept form.

2y = -5x + 10
y = (-5/2)x + 5

Therefore the slope is -5/2

1) Function

2) y = mx + b
You know b = -3 because b is the y intercept

y = 5x - 3

In standard form:

y - 5x = -3

3)
Slope = (y2 - y1) / (x2 - x1)
3 = (10 - y) / (5 - x)
15 - 3x = 10 - y
y - 3x = -5
or
y = 3x - 5

4)That was in your question heading, answer is at the top.

5)
2x + 5y = -10
5y = -2x - 10
y = (-2/5)x - 2

6)
Slope = Undefined

7)
Sketch the line of y = 2x - 3 on a graph.
The area above y = 2x - 3 should be shaded in. The line of y = 2x - 3 should NOT be included because it is >, not greater than or equal to
8)
4x - 3y = 12
Let y = 0
4x = 12
x = 3

X intercept (3, 0)

Let x = 0
-3y = 12
y = -4

Y intercept (0, -4)

9)
f(5) = 3(5) - 4
f(5) = 15 - 4
f(5) = 11

10)
Slope = (y2 - y1) / (x2 - x1)
Slope = (8 - 0) / (0 - 2)
Slope = 8 / -2
Slope = -4

11)
Same question as 10

12)
First find f(4)
f(4) = 2(4) + 1
f(4) = 8 + 1
f(4) = 9

now find g[f(4)]

g[f(4)] = 2x - 5
g(9) = 2(9) - 5
g(9) = 18 - 5
g(9) = 13

Answer 2

1. Function

2. y = m*x + b Plug in the values for m and b that are given to you in the problem: y = 5x - 3

3. y = 3x + b (3 came from the problem)
10 = 3*5 + b (substitution of the x,y values in the problem)
b = -5 (simple algebra)
y = 3x - 5

4. 2y = -5x + 10
y = -5/2 * x + 5
m = -5/2

5. 5y = -2x - 10
y = -2/5 * x - 2

6. Vertical lines have an undefined slope.

7. It is the area above the curve y = 2x - 3

8. 4x = 12
x = 3 (x-intercept)
-3y = 12
y = -4 (y-intercept)

9. 3(5) - 4 = 11

10. (2-0)/(0-8) = 2/-8 = -1/4

11. See # 10 since it's the same question.....

12. f(4) = 2(4)+1 = 9
g(9) = 2*9-5 = 13

Hope that helps and please pay attention in class. It makes the job of teachers like myself much easier.

Answer 3

1.) a function
2.) y=mx+b so you sub in 5 for m, 0 for x and -3 for y and solve for b
0=5(-3)+b
0=-15+b
15=b
equation of the line is y=5x+15
3.) same steps as question
y=mx+b
10=3(5)+b
10=15+b
-5=b
equation is y=3x-5
4.) 5x+2y=10, solve for y by subtracting 5x from both sides to get
2y=-5x+10, then divide both sides by 2 to get
y=-5/2+5, the slope of that line is -5/2
5.) 2x+5y=-10 to change it to slop-intercept form subtract 2x from both sides to get 5y=-2x-10, then divide both sides by 5 to get y=-2/5x-2
6.) the slope of a vertical line is always undefined, since x=5 is a vertical line, it is undefined
7.) here is the link to a picture of the graph i made, the shaded region represents the inequality... http://img.photobucket.com/albums/v240/___jack1yn03/graphh.jpg
8.)to find the x intercept plug in x=0 to the equation and solve for y....
4x-3y=12
4(0)-3y=12
0-3y=12divide both sides by -3 to get
y=-4 that is the X intercept
to find the y intercept plug in y=0 into the equation and solve for x
4x-3y=12
4x-3(0)=12
4x=12
x=3
9.) f(5) just means the in this equation all the x's are equal to 5 so plug in 5 wherever there is an x in the fuction...
f(5)=3(5)-4
f(5)=15-4
f(5)=11
10.) to find the slope use the formula m= y2-y1/ x2-x1
m=8-0/0-2
m=8/-2
m=-4
11.) you asked the same question twice...answer is the same as number 10
12.) g[f(4)] means you must first plug in 4 into all the x's in the f function...
f(x)=2x+1
f(4)=2(4)+1
f(4)=8+1
f(4)=9
the you plug in 9 into all the x's of the g function
g(x)=2x-5
g(9)=2(9)-5
g(9)=18-5
g(9)=13

hope this helped :)

Answer 4

When you have an equation for a line, rearrange it to slope-intercept form,
y = mx + b
Then m is the slope and b is the y-intercept.

For the line 5x + 2y = 10, isolate the y term by subtracting 5x from both sides of equation:
2y = -5x + 10
then divide both sides by 2 so the coefficient of y is 1:
y = -2.5x + 5

The slope is -2.5 and the y-intercept is 5

Answer 5

You should at least "try" doing your homework before asking for help...
Obviously you're lazy...