Question

What is the equation of the line with an x-intercept at 2 that contains the point (4,-5)

Answer 1

The standard equation of line is 5 x + 2 y = 10.

Explanation:

X - intercept = 2

Point given = (4,-5)

Now, since x intercept is 2

⇒ the other point that line contains = (2,0)

So, the two point line contains is A(2,0) and B(4,-5)

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

or,
`m  = (-5-0)/(4-2)  = -(5)/(2)`

⇒ the slope of AB is m = - (5/2)

By POINT SLOPE 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 (2,0) is

`y - 0 = -((5)/(2) )(x -2)\\\implies 2y + 5x = 10`

Hence, the standard equation of line is 5 x + 2 y = 10.