Transform y-6=2(3x+8) into slope intercept form
To transform the equation y-6=2(3x+8) into slope-intercept form (y=mx+b), we need to isolate y.
First, distribute 2 to (3x+8):
y-6=6x+16
Next, isolate y by moving -6 to the right side:
y=6x+16+6
Simplifying, we get:
y=6x+22
Therefore, the equation is now in slope-intercept form.
Graph y=3x+5
To graph the equation y=3x+5, we will utilize the slope-intercept form (y=mx+b).
The equation y=3x+5 tells us that the slope is 3, which means that for every 1 unit increase in the x-coordinate, the y-coordinate increases by 3 units.
To begin graphing, we can assign values to x and find the corresponding y-values.
When x=0:
y = 3(0) + 5 = 5
When x=-1:
y = 3(-1) + 5 = 2
When x=1:
y = 3(1) + 5 = 8
When x=-2:
y = 3(-2) + 5 = -1
When x=2:
y = 3(2) + 5 = 11
Plotting these points on the graph, we can connect them to form a straight line.
The graph of y=3x+5 is a line that passes through the points (0, 5), (-1, 2), (1, 8), (-2, -1), and (2, 11).
Graph y=-3x+5
To graph the equation y=-3x+5, we can use the slope-intercept form (y=mx+b).
The equation y=-3x+5 tells us that the slope is -3, which means that for every 1 unit increase in the x-coordinate, the y-coordinate decreases by 3 units.
To begin graphing, we can assign values to x and find the corresponding y-values.
When x=0:
y = -3(0) + 5 = 5
When x=-1:
y = -3(-1) + 5 = 8
When x=1:
y = -3(1) + 5 = 2
When x=-2:
y = -3(-2) + 5 = 11
When x=2:
y = -3(2) + 5 = -1
Plotting these points on the graph, we can connect them to form a straight line.
The graph of y=-3x+5 is a line that passes through the points (0, 5), (-1, 8), (1, 2), (-2, 11), and (2, -1).
Two dots only
If we only consider two points, we can choose any two points on the line.
Let's select the points (0, 5) and (1, 2).
Plotting these two points on the graph and connecting them with a straight line, we will see the graph of y=-3x+5.
Use two points and graph y=5/7x+2
To graph y=5/7x+2, we will use two points on the line.
Let's choose the points (0, 2) and (7, 7).
When x=0:
y = (5/7)(0) + 2 = 2
When x=7:
y = (5/7)(7) + 2 = 5 + 2 = 7
Plotting these two points on the graph and connecting them with a straight line, we can see the graph of y=5/7x+2.
Solve -3/y=20/9
y=?
To solve the equation -3/y = 20/9 for y, we can cross-multiply and then solve for y.
Cross-multiplying, we have:
-3 * 9 = y * 20
Simplifying, we get:
-27 = 20y
Dividing both sides of the equation by 20, we have:
y = -27/20
Therefore, the value of y is -27/20.
Using two points, graph y=-3/5x-4
To graph y=-3/5x-4, we can choose any two points on the line.
Let's select the points (0, -4) and (5, -7).
When x=0:
y = (-3/5)(0) - 4 = -4
When x=5:
y = (-3/5)(5) - 4 = -3 - 4 = -7
Plotting these two points on the graph and connecting them with a straight line, we can see the graph of y=-3/5x-4.
Using two points, graph x=-5
To graph x=-5, we can draw a vertical line passing through the x-coordinate -5.
Since the x-coordinate is always -5 regardless of the value of y, we can choose any two points on this vertical line.
For example, let's select the points (-5, 0) and (-5, 5).
Plotting these two points on the graph and connecting them with a straight line, we can see the graph of x=-5 as a vertical line passing through the point (-5, 0) and (-5, 5).
How to know if a graph is proportional and give a few examples of proportional equations
To determine if a graph is proportional, look for a linear relationship between the x and y values. If the ratio of the y values to the x values remains constant, the graph is proportional.
Mathematically, a graph is proportional if it can be represented by the equation y = kx, where k is a constant. In this case, as x increases, y increases or decreases in direct proportion.
Here are a few examples of proportional equations:
1) y = 2x: In this equation, y is twice the value of x. For every increase in x, y also increases by the same ratio of 2:1.
2) y = 0.5x: In this equation, y is half the value of x. For every increase in x, y also increases, but at a slower rate, with the ratio of 1:2.
3) y = -3x: In this equation, y is three times the negative of x. As x increases, y decreases proportionally by the ratio of -3:1.
These are just a few examples of proportional equations, and they exhibit the characteristic of constant ratios between the x and y values, indicating proportionality in their graphs.