Question 157640
Hi, Hope I can help
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write an equation in slope-intercept form for the line that satisfies the following condition. slope {{{ 1/3 }}} and passes through (3,9)
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The slope intercept form of an equation is equal to {{{ y = mx + b }}}, where "m" is the slope, "b" is the y intercept.
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We know the slope is {{{ 1/3 }}}, so we can replace "m" with {{{ 1/3 }}} in our equation
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{{{ y = mx + b }}}, becomes {{{ y = (1/3)x + b }}}, now we have to find "b"
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We now a point on the line, point (3,9), and because points are given as (x,y), we can use the point to solve for "b"
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If the point is (3,9)(x,y), all we need to do is replace "x" and "y" in our equation, with the numbers(replace "x" with "3", replace "y" with "9")
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{{{ y = (1/3)x + b }}}, becomes {{{ (9) = (1/3)(3) + b }}}
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{{{ (9) = (1/3)(3) + b }}} = {{{ (9) = (1) + b }}}
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{{{ (9) = (1) + b }}} = {{{ 9 = 1 + b }}}, to find "b" we will move "1" to the left side
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{{{ 9 = 1 + b }}} = {{{ 9 - 1 = 1 - 1 + b }}}
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{{{ 9 - 1 = 1 - 1 + b }}} = {{{ 8 = b }}} = {{{ b = 8 }}}
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We found that "b" = "8", we can replace "b" with "8" in our equation
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{{{ y = (1/3)x + b }}} = {{{ y = (1/3)x + 8 }}}
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{{{ y = (1/3)x + 8 }}} is the slope-intercept form/equation of the line
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We can check our answer by replacing "x" and "y" with (3,9)(x,y) in our equation
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{{{ y = (1/3)x + 8 }}} = {{{ (9) = (1/3)(3) + 8 }}}
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{{{ (9) = (1/3)(3) + 8 }}} = {{{ (9) = (1) + 8 }}}
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{{{ (9) = (1) + 8 }}} = {{{ 9 = 1 + 8 }}} = {{{ 9 = 9 }}} (True)
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We can also find that the y intercept(where the line hits the y-axis) is (0,8), another point on the line,
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We can check by replacing "x" and "y" with (0,8)(x,y),
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{{{ y = (1/3)x + 8 }}} = {{{ (8) = (1/3)(0) + 8 }}}
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{{{ (8) = (1/3)(0) + 8 }}} = {{{ (8) = (0) + 8 }}}
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{{{ (8) = (0) + 8 }}} = {{{ 8 = 0 + 8 }}} = {{{ 8 = 8 }}} (True)
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The slope-intercept form/equation of the line is {{{ y = (1/3)x + 8 }}}
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Hope I helped, Levi