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Question 595430: Write in slope-intercept form the equation of the line that passes through the given point and has the given slope.
(4,-2),m=1/2
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! The slope-intercept form is:
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and you are told that m, the slope, is  . Therefore, you can substitute for m in the equation to get:
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You are told that the point (4, -2) is on the line. That means that you know that when x is 4, then y is -2. So, you can substitute 4 for x and -2 for y in the equation. When you do that, you will be able to solve for b. So, when you do the substitutions for x and y the equation becomes:
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When you multiply 1/2 times 4, you get 2. So after this multiplication, the equation is:
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To get rid of the 2 on the right side, you can just add -2 to both sides. After doing that the equation is:
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Now you know the value of b is -4. Return to the slope-intercept equation:
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and substitute -4 for b and you have:
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As a final step, remove the parentheses around the -4, recognizing that the parentheses are preceded by a + sign so you just remove the + sign and the parentheses to get:
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and that's the slope-intercept equation that is the answer to the problem.
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Just aa a check, you can substitute 4 for x and you should get that y = -2 because the point (4, -2) is in the solution set.
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That checks, so your equation is correct.
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Hope this helps you to better understand this problem and how you can work it.
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