Question

What is the equation of the line that passes through P( 6,2) and S ( 3,1)?

Answer 1

`y=1/3x`

Explanation:

`"the equation of a line in "color(blue)"slope-intercept form"` is.

`•color(white)(x)y=mx+b`

`"where m is the slope and b the y-intercept"`

`"to calculate m use the "color(blue)"gradient formula"`

`•color(white)(x)m=(y_2-y_1)/(x_2-x_1)`

`"let "(x_1,y_1)=(6,2)" and "(x_2,y_2)=(3,1)`

`rArrm=(1-2)/(3-6)=(-1)/(-3)=1/3`

`rArry=1/3x+blarrcolor(blue)"is the partial equation"`

`"to find b substitute either of the 2 given points into"`
`"the partial equation"`

`"using "(3,1)" then"`

`1=1+brArrb=0`

`rArry=1/3xlarrcolor(red)"equation of line"`

Answer 2

`" "`
`color(blue)(y=1/3x` is

the required equation of the line

passing through the two points `color(red)(P(6,2)) and color(red)(S(3,1)`.

Explanation:

`" "`
`color(brown)("Given two points: " P(6,2) and S(3,1)`

`color(red)(y=mx+b` is

the equation in Slope-Intercept Form for a line.

Note:

`m` is the Slope (or) the Gradient

`y` is the dependent variable

`x` is the independent variable

`b` is the y-intercept.

`color(green)("Step 1:"`

To find the Slope:

Slope Formula: `color(blue)(m=(y_2-y_1)/(x_2-x_1)`

`color(brown)("Given points: " P(6,2) and S(3,1)` will be our `color(blue)((x_1, y_1) and (x_2, y_2)` respectively.

Hence `color(red)(x_1=6, y_1=2, x_2=3, y_2=1`

`Slope(m)=(1-2)/(3-6)`

`rArr( -1)/-3=1/3`

`color(blue)( :. m=1/3`

`color(green)("Step 2:"`

Find the value of `color(red)(b`

Choose one of the points give: `color(red)(S(3,1)`

Using this point: `color(blue)(x=3, y=1`

From the previous step: `m=1/3`

Substitute these values of `color(brown)(x,y and m` in `color(blue)(y=mx+b` to find `color(red)(b`.

`1=1/3(3)+b`

Simplifying

`1=1+b`

`color(blue)( :. b=0`

`color(green)("Step 3:"`

Obtain the equation of the line:

`y=1/3x`

Hence,

`color(blue)(y=1/3x` is

the required equation of the line

passing through the two points `color(red)(P(6,2)) and color(red)(S(3,1)`.

Hope it helps.