WEBVTT
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Write in the form π¦ equals ππ₯ plus π the equation of a line through negative one, negative one that is parallel to the line negative six π₯ minus π¦ plus four equals zero.
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So weβve been asked to find the equation of a line in slope-intercept form: π¦ equals ππ₯ plus π€.
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Weβve also been given two pieces of information about this line, which are the coordinates of a point on this line negative one, negative one.
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Weβre also told the key piece of information that this line is parallel to the line, whose equation is negative six π₯ minus π¦ plus four equals zero.
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So in order to answer this question, we need to determine the values of π and π for the line that weβre interested in.
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Letβs begin by thinking about π, the slope of the line.
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Weβre told that this line is parallel to the line, whose equation weβve been given.
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And so we need to remember the key fact that if two lines are parallel, then their slopes are the same.
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This means we can determine the value of π for our line by looking at the slope of the other line.
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Looking at the equation of the second line, itβs not quite in the right format for us to be able to determine its slope.
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We need to rearrange it into slope-intercept form.
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This only requires one step of working out.
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I need to add π¦ to both sides of the equation.
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And doing so, I have that π¦ is equal to negative six π₯ plus four.
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Now this line is in slope-intercept form.
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And if I compare it to π¦ equals ππ₯ plus π€, I can see that the slope of this line is negative six; itβs this value here β the coefficient of π₯.
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Remember the line weβre interested in is parallel to this line, so it has the same slope.
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This means that our line has the equation π¦ equals negative six π₯ plus π€, for a value of π€ that we now need to calculate.
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Remember that the point with coordinates negative one, negative one lies on our line.
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Phrased another way, this means that these values of π₯ and π¦, which here are both negative one, satisfy the equation of our line.
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So I can substitute these values into the equation in order to determine π€.
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So substituting negative one for both π₯ and π¦, we now have negative one is equal to negative six multiplied by negative one plus π, and this is an equation that I can solve.
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Negative six multiplied by negative one is positive six, so I have negative one is equal to six plus π.
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I now need to subtract six from both sides of the equation.
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And then doing so, I have that negative seven is equal to π.
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So we found the value of π€.
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The final step is I need to substitute this value of π€ into the equation of the line.
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So we have our answer to the problem.
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The equation of this line in slope-intercept form is π¦ is equal to negative six π₯ minus seven.
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Remember the key fact that weβve used in this question was that if two lines are parallel, then their slopes are equal.