Graph and then find the solution. for y= -1/2 x-6 and y= -7/6 x+4
To graph the equations y = -1/2 x - 6 and y = -7/6 x + 4, we can plot a few points for each equation and then connect them with a straight line.
For the first equation, y = -1/2 x - 6, we can choose three arbitrary x values and substitute them into the equation to find their corresponding y values:
When x = 0, y = -1/2(0) - 6 = -6.
When x = 2, y = -1/2(2) - 6 = -7.
When x = 4, y = -1/2(4) - 6 = -8.
So, we have the following points: (0, -6), (2, -7), (4, -8).
For the second equation, y = -7/6 x + 4, we can again choose three arbitrary x values and substitute them into the equation:
When x = 0, y = -7/6(0) + 4 = 4.
When x = 2, y = -7/6(2) + 4 = 1 1/3.
When x = 4, y = -7/6(4) + 4 = -1 1/3.
So, we have the following points: (0, 4), (2, 1 1/3), (4, -1 1/3).
Plotting these points on a graph and connecting them with lines gives us two intersecting lines:
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-10| *
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-8| *
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-6| *
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-4| *
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-2| *
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-4 -2 0 2 4 6 8 10 12 14
The solution to this system of equations is the coordinates of the point where the two lines intersect. By inspecting the graph, we can see that the intersection occurs at approximately (6, -9). Therefore, the solution to the system of equations is x = 6 and y = -9.
Find the slope and y-intercept that has infinite solutions to the equation
4x+ 10y= 25
The slope would be____
the y intercept would be____ . (do not list as a coordinate point.)
To determine the slope-intercept form of the equation 4x + 10y = 25, we need to solve it for y.
Starting with the given equation:
4x + 10y = 25
We want to isolate y, so we can subtract 4x from both sides:
10y = -4x + 25
Next, divide both sides by 10 to solve for y:
y = (-4/10)x + 25/10
Simplifying the equation further:
y = (-2/5)x + 5/2
Comparing this equation to the slope-intercept form y = mx + b, we can observe that the slope is -2/5 and the y-intercept is 5/2. Therefore, the slope is -2/5 and the y-intercept is 5/2.
Find the slope and y-intercept that has infinite solutions to the equation
-24x + 2y = 42
The slope would be ____
The y-intercept would be ____ (do not list as a coordinate point.)
To determine the slope-intercept form of the equation -24x + 2y = 42, we need to solve it for y.
Starting with the given equation:
-24x + 2y = 42
We want to isolate y, so we can add 24x to both sides:
2y = 24x + 42
Next, divide both sides by 2 to solve for y:
y = 12x + 21
Comparing this equation to the slope-intercept form y = mx + b, we can observe that the slope is 12 and the y-intercept is 21. Therefore, the slope is 12 and the y-intercept is 21.
Solve the following inequality.
-10/3 y ≤ 3
y drop down answers are ≤ or ≥, ______
To solve the inequality -10/3 y ≤ 3, we can begin by multiplying both sides of the inequality by -3/10 (the reciprocal of -10/3). However, it is important to note that when we multiply both sides of an inequality by a negative number, we need to reverse the direction of the inequality.
So, let's multiply both sides of the inequality -10/3 y ≤ 3 by -3/10:
(-10/3 y) * (-3/10) ≥ 3 * (-3/10)
Simplifying this, we get:
y ≥ -9/10
Therefore, the solution to the inequality is y ≥ -9/10.
Solve the following inequality.
-10(-5x +7) ≤7
x drop down answers are ≤ or ≥, _______
To solve the inequality -10(-5x + 7) ≤ 7, we can begin by simplifying the expression inside the parentheses.
First, distribute -10 to -5x and 7:
-10 * (-5x + 7) ≤ 7
50x - 70 ≤ 7
Next, add 70 to both sides to isolate the x term:
50x - 70 + 70 ≤ 7 + 70
50x ≤ 77
Finally, divide both sides by 50 to solve for x:
x ≤ 77/50
Therefore, the solution to the inequality is x ≤ 77/50.
Solve the following inequalities.
2x < 35
x and the drop down answers are < or >, ______
-2y < 35
y and then the drop down answers are < or >, ______
2x < -35
z and the drop down answers are < or >, ______