Find the Line Equation Through Points (1/3,1) and (-1/3,2): Coordinate Geometry

Question

Find the equation of the line passing through the two points $(\frac{1}{3},1),(-\frac{1}{3},2)$

00:00 Find the algebraic representation of the function

00:04 We'll use the formula to find the slope using 2 points

00:08 In each point, the left number represents X-axis and the right Y

00:16 We'll substitute the points according to the given data and find the slope

00:32 This is the line's slope

00:38 Now we'll use the line equation

00:43 We'll substitute the point according to the given data

00:47 We'll substitute the slope, and solve to find the intersection point (B)

01:03 We'll isolate the intersection point (B)

01:08 This is the intersection point with the Y-axis

01:14 Now we'll substitute the intersection point and slope in the line equation

01:23 And this is the solution to the question

In the first step, we'll find the slope using the formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

We'll substitute according to the given points:

$m=\frac{1-2}{\frac{1}{3}-(-\frac{1}{3})}$

$m=\frac{-1}{\frac{2}{3}}=-\frac{3}{2}$

Now we'll choose point $(\frac{1}{3},1)$ and use the formula:

$y=mx+b$

$1=-\frac{3}{2}\times\frac{1}{3}+b$

$1=-\frac{1}{2}+b$

$b=1\frac{1}{2}$

We'll substitute the given data into the formula to find the equation of the line:

$y=-\frac{3}{2}x+1\frac{1}{2}$

$y=-\frac{3}{2}x+1\frac{1}{2}$