# Video: Finding the Equation of a Line given Its Slope and a Point on the Line

A line πΏ has a slope of β2 and passes through the point (2, β3). Work out the equation of the line, giving your answer in the form π¦ = ππ₯ + π.

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### Video Transcript

A line πΏ has a slope of negative two and passes through the point two, negative three. Work out the equation of the line, giving your answer in the form π¦ equals ππ₯ plus π.

So weβve been given two pieces of information about this line. First of all, weβre told the slope of the line. Weβre also told the coordinates of one point on the line. Weβve also been asked to give our answer in a particular form π¦ equals ππ₯ plus π, which is slope-intercept form. Remember π represents the slope of the line and π represents the π¦-intercept. So what we need to do within this question is determine the values of π and π.

Weβve actually been given the value of π within the question itself as weβre told that itβs equal to two. This means that straightaway we can substitute the value of π into the equation of the line. So we have that π¦ is equal to negative two π₯ plus π.

Now, we need to determine the value of π, the π¦-intercept of the line. To do this, weβll use the coordinates of the point that we know lies on the line. This point satisfies the equation of the line, which means that when π₯ is equal to two, π¦ is equal to negative three within this equation. We can therefore substitute the values of π₯ and π¦ in order to find the value of π. So by substituting π₯ equals two and π¦ equals negative three, we now have the equation negative three is equal to negative two multiplied by two plus π.

And here is the equation that we can solve to find the value of π. Negative two multiplied by two is negative four. So now we have negative three is equal to negative four plus π. In order to determine π, I need to add four to both sides of the equation. And this tells me that π is equal to one.

The final step is I need to substitute this value of π into the equation of the line. So this gives us our answer to the problem. The equation of this line in slope-intercept form is π¦ is equal to negative two π₯ plus one.