Question 118341: White each equation in slope-intercept form.
#9 3.4
3x - 4y = 80
#21 3.4
find the equation of the line that goes through the given point and has the given slope. Write the answer in slope-intercept form.
(-1, -7), -6
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! For reference:
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The slope-intercept form of an equation is y = mx + b
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In this form, m (the multiplier of x) is the slope of the line and b (a constant) is the
value on the y-axis where the line intercepts the y-axis.
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Given for the first problem:
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Notice in the slope intercept form you want y to be by itself on the left side of the equal
sign. So for this problem we begin by getting rid of the 3x term on the left side by subtracting
3x from both sides of the equation. After subtracting 3x from both sides you are left with:
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To just have y on the left side, you now divide both sides (all terms) by -4 and you get:
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In the fraction that multiplies x you have a minus sign in both the numerator and the
denominator. Since this means you are dividing two minus quantities, the answer will be
positive and you end up with the answer to this problem ... the slope-intercept form of:
.
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in which the slope (or multiplier of x) is  and the place where the graphed line
for this equation crosses the y-axis is at +80 on the y-axis.
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Again, the answer to the first problem is:
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For the second problem you to find the slope-intercept equation of a line that goes through
the point (-1, -7) and has a slope equal to -6.
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Again, the slope intercept form equation is y = mx + b where m is the slope. Since the
problem tells you that the slope is -6 you can substitute that value for m to get:
.
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Next, you need to solve for b. You are told by the problem that when x equals -1 and y equals -7
the equation for the line will be satisfied. That is because the (x, y) point (-1, -7) is on
the line. So substitute -1 for x and -7 for y to get that:
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becomes:
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Do the multiplication on the right side ... -6 times -1 and the equation becomes:
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Get rid of the +6 on the right side by subtracting 6 from both sides and the result is:
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Now that you know that b = -13 you can return to the equation:
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and substitute -13 for b to get that the slope-intercept form of the equation that has a
slope of - 6 and goes through the point (-1, -7) is:
.
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and this is the answer to the second problem. You can check it by substituting -1 for x
and find out if the corresponding value of y is -7 ... just as you were told it should be
in the problem. (It is, so the problem checks.)
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Hope this helps you to understand the two problems and how you can solve them both.
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