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Question 117996: Find the equation of the line that goes through the given point and has the given slope. Write the answer in slope-intrecept form.
(-1,-5),-8
this is what I did
-5y=-8x + -1 I got b= -13 which is incorrect
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! The slope intercept form of an equation is:
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y = mx + b
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where m is the slope and b is the point on the y-axis at which the line crosses the y-axis.
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In this problem you are told that the line is to have a slope of -8. So you substitute
-8 for m in the slope intercept form and you get:
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y = -8x + b
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You are also told that the point (-1, -5) must be on the line. This means that the equation
must be true when x equals -1 and y equals -5. So in the slope intercept form you replace x by
-1 and y by -5 to get:
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-5 = -8(-1) + b
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Do the multiplication on the right side and this equation becomes:
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-5 = 8 + b
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Get rid of the 8 on the right side by subtracting 8 from both sides and you are left with:
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-13 = b
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This value for b is then substituted into the slope intercept equation that was written above:
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y = -8x + b
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and when you replace b by -13 the equation becomes:
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y = -8x - 13
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By inspection you can see that the slope of this line (the multiplier of x) is -8 and the
line crosses the y-axis at y = -13.
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As a check, in this equation replace x by -1 to get:
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y = -8(-1) - 13
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Do the multiplication on the right side and it becomes:
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y = +8 - 13
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Add the two numbers on the right side and you get:
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y = -5
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So when x equals -1 the corresponding value of y is -5. This tells you that the point (-1, -5)
is on the graph. So the answer is correct. The answer is:
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y = -8x - 13
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Hope this problem helps you understand the slope intercept form a little better.
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