Question

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Answer 1

`y = (1)/(2) x + (1)/(2)`

Explanation:

equation of line formula:

`y = mx + c`

m = slope

c = y-intercept

1) find m

slope formula:

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

take 2 coordinates from the given graph and substitute the values into the slope formula

i) (-1,0)

`x _(1) = - 1`

`y_(1) = 0`

ii) (3,2)

`x_(2) = 3`

`y_(2) = 2`

substitute the values into the slope formula

`m = (2 - 0)/(3 - ( - 1))`

`m = (2)/(4)`

`m = (1)/(2)`

2) find the half equation of the line by substituting the value of m into the equation of line formula

`y = (1)/(2) x + c`

3) find c by substituting either coordinate into the half equation

(3,2)

x = 3

y = 2

`2 = (1)/(2) (3) + c`

`2 = (3)/(2) + c`

`2 - (3)/(2) = c`

`(1)/(2) = c`

`c = (1)/(2)`

4) find equation of line by substituting the value of c into the half equation

`y = (1)/(2) x + (1)/(2)`