Question

What is the y-intercept of theline that passes through the points (2, 5) and (3, 6)

(0, -7)
(0, -3)
(0, 1)
(0, 3)

Answer 1

The y-intercept is ( 0 , 3 ) .

Explanation:

Given as :

The points are

`x_1` ,
`y_1` = 2 , 5

`x_2` ,
`y_2` = 3 , 6

Let The slope of line with these points = m

So, Slope of line =
`(y_2 - y_1)/(x_2 - x_1)`

i.e m =
`(y_2 - y_1)/(x_2 - x_1)`

Or, m =
`(6 - 5)/(3 - 2)`

Or, m =
`(1)/(1)`

∴ m = 1

So, The slope = m = 1

Now, Equation of line with points
`x_1` ,
`y_1` and slope m can be written as

y - tex]y_1[/tex] = m × ( x - tex]x_1[/tex] )

i.e y - 5 = 1 × ( x - 2 )

Or, y - 5 = x - 2

Or, y = x - 2 + 5

So, The equation of line is

y = x + 3

Again

For y - intercept

Put x = 0 in the line equation

∵ y = x + 3

Or, y = 0 + 3

∴ y = 3

So, The y - intercept = ( x , y ) = ( 0 , 3 )

Hence, The y-intercept is ( 0 , 3 ) . Answer