Write the slope-intercept equation for the line with slope -2/3 and y-intercept (0, 3) and graph the line. Please show all of your work. (
Thanks Drbob222
To find the slope-intercept equation of a line, we use the formula: y = mx + b, where m is the slope and b is the y-intercept.
Given that the slope is -2/3 and the y-intercept is (0, 3), we can substitute these values into the formula.
The slope, m, is -2/3, so the equation becomes: y = (-2/3)x + b.
Next, we substitute the y-intercept, (0, 3), into the equation to find the value of b. When x = 0, y = 3.
So, substituting these values into the equation, we get: 3 = (-2/3)(0) + b.
Since anything multiplied by 0 is 0, the equation simplifies to: 3 = 0 + b.
Therefore, b = 3.
Now that we have the values for m and b, we can write the final slope-intercept equation: y = (-2/3)x + 3.
To graph this line, we first plot the y-intercept at (0, 3), which is the point (0, b) on the line.
Next, we use the slope to find another point on the line. The slope is -2/3, which means that for every 3 units we move horizontally to the right, we move 2 units vertically downward.
So, starting from (0, 3), we move 3 units to the right (since 3/3 = 1) and 2 units downward. This gives us the point (3, 1) on the line.
Finally, we draw a straight line passing through these two points, extending it in both directions. This line represents the equation y = (-2/3)x + 3.
Graphically, the line should look like this:
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| (3, 1)
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| (0, 3)
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Hope this helps! Let me know if you have any further questions.
To find the slope-intercept equation of a line, we need two pieces of information: the slope (m) and the y-intercept (b).
Given that the slope (m) is -2/3 and the y-intercept (b) is (0, 3), we can use these values to write the equation.
The slope-intercept form of a line is given by y = mx + b, where m represents the slope, and b represents the y-intercept.
So, to write the equation using the given values, we have:
y = (-2/3)x + 3
Now let's graph the line:
To graph the line, we need to plot the y-intercept first, which is (0, 3). This point represents where the line intersects the y-axis. So, we plot this point on the graph.
Next, we can use the slope to find another point on the line. The slope of -2/3 means that for every 2 units we move down, we move 3 units to the right. This gives us a negative slope, as we move downward.
Starting from the y-intercept (0, 3), we can move 2 units down and 3 units to the right to find another point. This would give us the coordinates (3, 1).
Now, we can connect the two points on the graph using a straight line. We can extend this line in both directions to represent the entire line.
So, the slope-intercept equation for the line with a slope of -2/3 and a y-intercept of (0, 3) is y = (-2/3)x + 3.
y = mx + b
m is the slope which is -2/3 and b is the y intercept which is 3. Substitute and you have it.