Graph the equation 3x-y=10.
To graph the equation 3x - y = 10, we need to rewrite it in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
Firstly, subtract 3x from both sides of the equation:
-y = -3x + 10
Next, multiply both sides by -1 to isolate y:
y = 3x - 10
Now, we can identify the slope and y-intercept. The slope is 3, meaning the line goes up 3 units for every 1 unit it goes to the right. The y-intercept is -10, which indicates that the line crosses the y-axis at -10.
To graph this line, plot the y-intercept at (0, -10) and use the slope to find other points. For example, starting at (0, -10), you can move 1 unit to the right and 3 units up to get to the point (1, -7). Similarly, from (1, -7), move again 1 unit to the right and 3 units up to reach (2, -4). Repeat this process multiple times to get a collection of points that line on the graph.
Here is the graph of the equation 3x - y = 10:
Graph:
To graph the equation 3x - y = 10, we need to rearrange it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Step 1: Start with the equation 3x - y = 10
Step 2: Add y to both sides to isolate the x term: 3x = y + 10
Step 3: Subtract 10 from both sides to isolate the y term: 3x - 10 = y
Step 4: Rewrite the equation in slope-intercept form: y = 3x - 10
Now that we have the equation in slope-intercept form, we can easily graph it.
Step 5: Plot the y-intercept: The y-intercept is the value of y when x = 0. From the equation, we can see that y = -10 when x = 0. So, plot the point (0, -10) on the graph.
Step 6: Determine the slope: The slope is the coefficient of x, which is 3 in this case. The slope of 3 means that for every increase of 1 in x, the y-value will increase by 3.
Step 7: Use the slope to find additional points: Starting from the y-intercept (0, -10), we can move horizontally 1 unit to the right (increase x by 1) and vertically 3 units up (increase y by 3) to reach another point. This gives us the point (1, -7). Similarly, we can use the slope to find other points, such as (2, -4), (3, -1), etc.
Step 8: Plot the points and draw a line: Plot all the points we found on the graph and connect them with a straight line. This line represents all the possible solutions to the equation 3x - y = 10.
Your graph should resemble a straight line that rises from left to right.
To graph the equation 3x - y = 10, we can follow these steps:
Step 1: Convert the equation to slope-intercept form (y = mx + b), where 'm' represents the slope and 'b' represents the y-intercept.
Given equation: 3x - y = 10
Subtract 3x from both sides: -y = -3x + 10
Multiply both sides by -1: y = 3x - 10
Step 2: Plot the y-intercept:
The y-intercept is the point at which the line intersects the y-axis. In this case, when x = 0, we can find the y-coordinate.
Using the equation, y = 3x - 10, substitute x = 0:
y = 3 * 0 - 10
y = -10
So, the y-intercept is (0, -10).
Step 3: Determine the slope:
The slope (m) represents the steepness of the line. In this equation, the coefficient of x is 3, so the slope is 3.
Step 4: Plot additional points:
To find more points, we can choose various x-values and substitute them into the equation to calculate the corresponding y-values. Let's select x = -2, 2, and 4:
For x = -2: y = 3 * -2 - 10 = -16, so the point is (-2, -16).
For x = 2: y = 3 * 2 - 10 = -4, so the point is (2, -4).
For x = 4: y = 3 * 4 - 10 = 2, so the point is (4, 2).
Step 5: Plot the points and draw the line:
Now that we have multiple points, we can plot them on a coordinate plane and draw a line passing through them.
The graph should include the points: (0, -10), (-2, -16), (2, -4), and (4, 2).
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-10 |•
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-2 0 2 4 6
x-axis
The line passing through these points represents the graph of the equation 3x - y = 10.