Question

How do you write the equation of the line in slope intercept form passing through (1, 2) and (2, 5)?

Answer 1

y = 3x -1

Explanation:

1. Find the slope by using the formula `(y_2-y_1)/(x_2-x_1)`
   You wil get: `(5-2)/(2-1)`
   Simplify to get 3

2. Find the y-intercept by plugging in one kf the pairs and the slope into the y = mx + b equation. It doesn’t matter which pair you use.

You see 2 = 3(1) + b
Solve for b
2 = 3 + b
-1 = b

1. Answer is y = 3x -1

Answer 2

`y=3x-1`

Explanation:

the gradient/slope is the difference in the `y` values divided by the difference in the `x` values.

`=>` `[5-2]/[2-1]` =`3/1` =3

so the equation of the line is `y=3x+c`

Use (1,2) `=>` `2=3xx1+c`
`=>` `2=3+c` so `c`=-1

this gives `y=3x-1`

Answer 3

`y=3x-1`

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)=(1,2)" and "(x_2,y_2)=(2,5)`

`rArrm=(5-2)/(2-1)=3`

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

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

`"using "(1,2)" then"`

`2=3+brArrb=2-3=-1`

`rArry=3x-1larrcolor(red)"equation in slope-intercept form"`