Q:

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

Accepted Solution

A:
Answer:The standard equation of line is  5 x + 2 y = 10.Step-by-step 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 = [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]or, [tex]m  = \frac{-5-0}{4-2}  = -\frac{5}{2}[/tex]⇒ 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[tex]y - 0 = -(\frac{5}{2} )(x -2)\\\implies 2y + 5x = 10[/tex]Hence, the standard equation of line is  5 x + 2 y = 10.