Sammie W. answered • 08/11/22
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How do I find slope-intercept form of a line passing through the point (1,3) with slope m = -2 and graph it?
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Hello, thank you for taking the time to post your question!
The general slope-intercept form is y = mx + b, so to find the value of “b” you can plug in the other values that we know from the information in the question
3 = -2(1) + b
3 = -2 + b
5 = b
Putting it all together then the equation is y = -2x + 5
To graph then I would start by plotting the y-intercept, then using the slope to find additional points.
Hopefully that gets you moving in the right direction! Feel free to reach out for a lesson if you have any questions beyond that! :)
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Ralph W.
The slope-intercept form of a linear equation is given by: \(y = mx + b\), where \(m\) is the slope of the line and \(b\) is the y-intercept (the value of \(y\) when \(x = 0\)). In your case, you have a slope \(m = -2\) and a point \((1, 3)\) that the line passes through. To find the equation in slope-intercept form, you need to determine the value of \(b\). Start with the equation \(y = mx + b\). Substitute the given point \((1, 3)\) into the equation: \(3 = -2 \cdot 1 + b\) Now solve for \(b\): \(b = 3 + 2 = 5\) So, the equation of the line in slope-intercept form is \(y = -2x + 5\). To graph this line, you can plot the point \((1, 3)\) on the coordinate plane and then use the slope to determine the direction of the line. Since the slope is negative (\(-2\)), the line will slope downward from left to right. Here's how to graph it: 1. Plot the point \((1, 3)\) on the coordinate plane. 2. Use the slope to find another point on the line. Since the slope is \(-2\), you can move one unit to the right and two units downward from the point \((1, 3)\). This gives you the point \((2, 1)\). 3. Draw a straight line passing through the two points \((1, 3)\) and \((2, 1)\). This line represents the equation \(y = -2x + 5\). Your graph should show a line that slopes downward from left to right and passes through the points \((1, 3)\) and \((2, 1)\).08/20/23