# The points (4,1) and (x,-6) lie on the same line. If the slope of the line is 1, what is the value of X?

Relevance
• The following equation is used to determine the slope of a line.

Slope = (y2 – y1) ÷ (x2 – x1)

1 = -7 ÷ (x2 – 4)

x2 – 4 = -7

x2 = -3

I hope this is helpful for you.

• :-

1 = ( - 7 ) / ( x - 4 )

x - 4 = - 7

x = - 3

• How to get the equation of the line that passes through A (4 ; 1) B (x ; - 6) ?

The typical equation of a line is: y = mx + y₀ → where m: slope and where y₀: y-intercept

m = (yB - yA) / (xB - xA)

m = (- 6 - 1) / (x - 4)

m = - 7/(x - 4) → given that it's 1

- 7/(x - 4) = 1

- 7 = x - 4

- 7 + 4 = x

x = - 3 ← this is the abscissa of the point B

To go further.

As the slope of the line (AB) is (1), the equation of the line (AB) becomes: y = x + y₀

The line (AB) passes through A, so these coordinates must verify the equation of the line (AB).

y = x + y₀

y₀ = y - x → you substitute x and y by the coordinates of the point A (4 ; 1)

y₀ = 1 - 4

y₀ = - 3

→ The equation of the line (AB) is: y = x - 3