Question

Find the equation of a line which passes through (2 4) with a slope of ½​

Answer 1

The answer is:

y = 1/2x + 5

Work/explanation:

Since I have a point and the slope, I will write the equation in point slope form.

Point slope is

`\sf{y-y_1=m(x-x_1)}`

where m = slope and (x₁, y₁) is a point on the line

Plug in the data

`\sf{y-4=(1)/(2)(x-2)}`

Now let's simplify to slope intercept

`\large\begin{gathered}\sf{y-4=(1)/(2)x+1}\\\sf{y=(1)/(2)x+1+4}\\\sf{y=(1)/(2)x+5}\end{gathered}`

Hence, the equation is y = 1/2x + 5.

Answer 2

The equation of the straight line is x - 2y +6 =0

Step-by-step explanation:

Step-by-step explanation:-

Given a point ( 2, 4) and slope m =
`(1)/(2)`

The equation of the straight line passing through the point and having slope 'm'

y - y₁ = m ( x - x₁)

y - 4 =
`(1)/(2)` ( x - 2)

2( y -4) = ( x-2)

2 y - 8 = x -2

x - 2 y - 2 + 8 =0

x - 2y + 6 =0

The equation of the straight line is x - 2y +6 =0