Question

Write the slope intercept equation that goes through (5, 1) and has a slope of 1/2

What is the x-intercept?
What is the y-intercept?​

Answer 1

see explanation

Explanation:

the equation of a line in slope- intercept form is

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

here m =
`(1)/(2)` , then

y =
`(1)/(2)` x + c ← is the partial equation

to find c substitute (5, 1 ) into the partial equation

1 =
`(5)/(2)` + c ⇒ c = 1 -
`(5)/(2)` = -
`(3)/(2)`

y =
`(1)/(2)` x -
`(3)/(2)` ← equation of line

to find the y- intercept , let y = 0 in the equation , that is

`(1)/(2)` x -
`(3)/(2)` = 0 ( multiply through by 2 to clear the fractions )

x - 3 = 0 ( add 3 to both sides )

x = 3 ← is the x- intercept

from the equation the y- intercept is the value of c , then

y- intercept = -
`(3)/(2)`