WEBVTT
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Find, in slope-intercept form, the equation of a line parallel to π¦ equals negative eight-thirds π₯ plus three, that passes through point π΄: negative three, two.
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To solve this problem, we can use the point slope formula.
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The point slope formula says π¦ minus π equals π times π₯ minus π, where π equals the slope and π, π is the given point.
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In our problem, weβve been given both, the point and the slope.
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You might be curious what the slope is since our question doesnβt explicitly say the slope.
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Thatβs okay because our question tells us that the line is parallel to π¦ equals negative eight-thirds π₯ plus three.
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And we know that parallel lines have the same slope.
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The slope of the line π¦ equals negative eight-thirds π₯ plus three is negative eight-thirds.
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And since parallel lines have the same slope, the slope of our line is also negative eight-thirds.
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We have a slope.
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Now we also have a point, negative three, two.
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Letβs plug everything in.
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Plug in two for π, so π¦ minus two equals negative eight-thirds, plugged in for π, times π₯ minus negative three.
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Negative three, itβs been plugged in for π.
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Now we can simplify this equation.
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Weβll say that π₯ minus negative three equals π₯ plus three.
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Then we need to distribute our negative eight-thirds, to π₯ and three.
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Negative eight-thirds times π₯ equals negative eight-thirds π₯.
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Negative eight-thirds times three equals negative eight.
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Weβre nearly there with our slope intercept form.
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But for slope intercept form, we need π¦ by itself.
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To do that, we add two to both sides of our equation.
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On the left, weβre left with π¦ and on the right, negative eight-thirds π₯ minus six.
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The equation of a line parallel to π¦ equals negative eight-thirds π₯ plus three β that also passes through point negative three, two β equals negative eight-thirds π₯ minus six.