Question

Slope is 1/4 and (16,4) is a point on the line

Answer 1

Our answer is y = 1/4x.

`\Large\texttt{Explanation}`

We are asked to find the equation of a line, given that

⇒ the slope of this line is 1/4

⇒ the point on the line is (16,4)

Use the point-slope formula (below) to find the equation.

`\bullet\quad\boldsymbol{y-y_1=m(x-x_1)}`

Substitute the values

`\boldsymbol{y-4=\cfrac{1}{4}(x-16)}`

`\boldsymbol{y-4=\cfrac{1}{4}x-4}`

`\boldsymbol{y=\cfrac{1}{4}x-4+4}`

`\boldsymbol{y=\cfrac{1}{4}x}`

`\therefore` the equation of this line is y = 1/4x

Answer 2

y =
`(1)/(4)` x

Explanation:

Assuming you require the equation of the line.

the equation of a line in slope- intercept form is

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

given slope m =
`(1)/(4)` , then

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

to find c, substitute (16, 4 ) for x and y in the partial equation

4 =
`(1)/(4)` (16) + c = 4 + c ( subtract 4 from both sides )

0 = c

y =
`(1)/(4)` x ← equation of line