Question

find the slope intercept and y intercept that has infinite soultions to the equation

8x+5y=15
Answer
find the slope intercept and the y intercept that has infinite solutions to the equation.

-24x+2y=46
Answer
solve the following inequality.

-2/4y is less than or equal to 4

y is greater than or equal to ?
Answer
solve the following inequality

-5(-10x+8) less than or equal to 3

x is less than or equal to ?
Answer
solve the following inequalities

10x<30
x<?

-10y,30
y>?

10z<-30
z<?
Answer
graph and then find the solution for y=1/2x+2 and y=-1/4x+8

Answered by GPT 3.5
To find the slope-intercept form of the equation, we need to solve for y.

8x + 5y = 15
5y = -8x + 15
y = (-8/5)x + 15/5
y = (-8/5)x + 3

The equation is now in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

The slope is -8/5 and the y-intercept is 3.

Since there is only one value for the y-intercept, there are no infinite solutions.
Answered by GPT 3.5
To find the slope-intercept form of the equation, we need to solve for y.

-24x + 2y = 46
2y = 24x + 46
y = (24/2)x + 46/2
y = 12x + 23

The equation is now in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

The slope is 12 and the y-intercept is 23.

To have infinite solutions, the given equation needs to be equivalent to another equation in slope-intercept form with the same slope and y-intercept.

However, the slope-intercept form of the equation clearly has only one unique slope (12) and y-intercept (23), so there are no infinite solutions.
Answered by GPT 3.5
To solve the inequality, multiply both sides of the inequality by 4 to eliminate the fraction.

(-2/4y) * 4 ≤ 4 * 4

-2y ≤ 16

Next, divide both sides of the inequality by -2, remembering that when you divide by a negative number, you must reverse the inequality sign.

(-2y) / -2 ≥ 16 / -2

y ≥ -8

So, the solution to the inequality is y ≥ -8.
Answered by GPT 3.5
To solve the inequality, first simplify the expression inside the parentheses by distributing the -5:

-5(-10x + 8) ≤ 3

50x - 40 ≤ 3

Next, add 40 to both sides of the inequality to isolate the x term:

50x - 40 + 40 ≤ 3 + 40

50x ≤ 43

Finally, divide both sides of the inequality by 50 to solve for x:

(50x) / 50 ≤ 43 / 50

x ≤ 43/50

So, the solution to the inequality is x ≤ 43/50.
Answered by GPT 3.5
To solve the inequality 10x < 30, divide both sides of the inequality by 10:

x < 3

So, the solution to the inequality is x < 3.

To solve the inequality -10y < 30, divide both sides of the inequality by -10. Remember to reverse the inequality sign when dividing by a negative number:

y > -3

So, the solution to the inequality is y > -3.

To solve the inequality 10z < -30, divide both sides of the inequality by 10:

z < -3

So, the solution to the inequality is z < -3.
Answered by GPT 3.5
To graph the equations y = (1/2)x + 2 and y = (-1/4)x + 8, we can plot points on a graph and connect them to form the lines.

For the equation y = (1/2)x + 2:
Let's choose a few x-values and substitute them into the equation to find the corresponding y-values:

When x = 0, y = (1/2)(0) + 2 = 2
When x = 2, y = (1/2)(2) + 2 = 3
When x = -2, y = (1/2)(-2) + 2 = 1

Plotting these points, we get:

(0, 2)
(2, 3)
(-2, 1)

Next, let's do the same for the equation y = (-1/4)x + 8:

When x = 0, y = (-1/4)(0) + 8 = 8
When x = 4, y = (-1/4)(4) + 8 = 7
When x = -4, y = (-1/4)(-4) + 8 = 9

Plotting these points, we get:

(0, 8)
(4, 7)
(-4, 9)

Now, we can connect these points to form the lines:

The line for y = (1/2)x + 2 is a straight line that rises as x increases, passing through the points (0, 2), (2, 3), and (-2, 1).

The line for y = (-1/4)x + 8 is a straight line that falls as x increases, passing through the points (0, 8), (4, 7), and (-4, 9).

Here is the graph:

|
10
8 | o /
|
6 | o /
|
4 | / /
| o /
2 | o /
___________________
-4 -2 0 2 4 6

The solution to these equations is the point where the two lines intersect, which occurs at approximately (4, 7).