Question Video: Finding the Equation of a Line given Two Points on the Line | Nagwa Question Video: Finding the Equation of a Line given Two Points on the Line | Nagwa

# Question Video: Finding the Equation of a Line given Two Points on the Line Mathematics • First Year of Secondary School

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A line πΏ passes through the points (3, 3) and (β1, 0). Work out the equation of the line, giving your answer in the form ππ¦ + ππ₯ + π = 0.

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### Video Transcript

A line πΏ passes through points three, three and negative one, zero. Work out the equation of the line, giving your answer in the form ππ¦ plus ππ₯ plus π equals zero.

What weβre going to do first, is work out the equation of the line. And after that, weβll focus on moving it into the form ππ¦ plus ππ₯ plus π.

To solve this problem, weβll need a few things. Letβs start with finding the slope and the π¦-intercept. The formula for finding slope is, the changes in π¦ over the changes in π₯. And we write that, π¦ two minus π¦ one over π₯ two minus π₯ one. We plug in these two points for our formula for finding slope. π¦ two is zero, minus π¦ one, which is three. π₯ two is negative one, minus π₯ one, which is three. We end up with negative three over negative four. We can simplify our slope to π equals three-fourths.

Now that we know our π is three-fourths, we can use this slope intercept form to find the intercept of this equation, to find our π. So we take our point negative one, zero and we plug those values in for π₯ and π¦. This gives us zero equals three-fourths times negative one plus π. When I multiply negative one by three-fourths, I get negative three-fourths. To get π by itself, I add three-fourths to the right side of the equation. And if I add three-fourths to the right side of the equation, I need to add three-fourths to the left side of the equation. This means that our π¦-intercept equals three-fourths, π equals three-fourths.

So we use this formula, and we plug in the π and π that we found. This gives us π¦ equals three-fourths π₯ plus three-fourths. Now we need to convert the slope intercept form into ππ¦ plus ππ₯ plus π equals zero. This means that weβll move everything to the left side of the equation, leaving only zero on the right side of the equation. We start that by subtracting three-fourths π₯ from both sides of the equation. This leaves us with π¦ minus three-fourths π₯ equals three-fourths. Then I can subtract three-fourths from both sides of the equation, which leaves me with π¦ minus three-fourths π₯ minus three-fourths equals zero.

But this is not our final answer. Because when we work with a form like this, we want π, π, and π to be integers, which means we donβt wanna have fractions like three-fourths as π or π. To fix this problem, we can multiply our entire form by four. We distribute the four to each term in the equation. Four times π¦ equals four π¦. Four times negative three-fourths equals negative three. Four times negative three-fourths equals negative three. Four times zero equals zero.

This is the equation of line πΏ written as ππ¦ plus ππ₯ plus π. We would write four π¦ minus three π₯ minus three equals zero.

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