Question

A line passes though the point (1,2) and crosses the y-axis at y=1. Which of the following is an equation for this line

A. y=2x
B.y=x+1
C. x+y=1
D. x/2-2

Answer 1

y = x + 1

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (1, 2 ) and (x₂, y₂ ) = (0, 1 ) ← point where it crosses y- axis

m =
`(1-2)/(0-1)` =
`(-1)/(-1)` = 1

the y- intercept is the value of y where the line crosses the y - axis

this is at y = 1 ⇒ c = 1

y = x + 1 ← equation of line