Find the Line Equation Through Points (5,0) and (1/2,4.5): Coordinate Method

Question

Find the equation of the line passing through the two points $(5,0),(\frac{1}{2},4\frac{1}{2})$

00:00 Find the algebraic representation of the function

00:03 We'll use the formula to find slope using 2 points

00:09 In each point, the left number represents X-axis and right Y

00:17 We'll substitute the points according to given data and find the slope

00:34 This is the line's slope

00:41 Now we'll use the line equation

00:45 We'll substitute the point according to given data

00:48 We'll substitute the slope, and solve to find the intersection point (B)

00:58 We'll isolate the intersection point (B)

01:04 This is the intersection point with the Y-axis

01:08 Now we'll substitute the intersection point and slope in the line equation

01:24 We'll arrange the equation

01:31 And this is the solution to the question

First, we will use the formula to find the slope of the straight line:

We replace the data and solve:

$\frac{(0-4.5)}{(5-0.5)}=\frac{-4.5}{4.5}=-1$

Now, we know that the slope is $-1$

We replace one of the points in the formula of the line equation:

$y=mx+b$

$(5,0)$

$0=-1\times5+b$

$0=-5+b$

$b=5$

Now we have the data to complete the equation:

$y=-1\times x+5$

$y=-x+5$

$y+x=5$