Question

What is the equation of the line shown below?

Answer 1

The equation of line in SLOPE INTERCEPT is y = x -1

Explanation:

Here, two points given on the line equation are

A(5,4) and B(-4,-5)

Now The slope of the line AB =
`m = (y_2 - y_1)/(x_2 - x_1)`

or,
`m = (-5 -4)/(-4 -5)  = (-9)/(-9)  = 1`

⇒ the slope of AB is m = 1

By SLOPE INTERCEPT FORMULA:

The equation of a line with slope m and a point (x0, y0) is given as

(y-y0)= m (x-x0)

⇒ The equation of line with point (5,4) is:

(y - 4) = (1) (x -5)

or, y - 4 = x - 5

⇒ y = x - 5 + 4

Now, SLOPE INTERCEPT FORM of a line equation is y = mx + c

⇒ y = x -1

Hence, the equation of line in SLOPE INTERCEPT is y = x -1