Question

What is the equation of the line that passes through the points `(4, 7)` and `(-2, 6)`?

Answer 1

`x-6y+38=0`

Explanation:

The equation of straight line passing through the given points `(x_1, y_1)\equiv(4, 7)` & `(x_2, y_2)\equiv(-2, 6)` is given by following formula

`y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)`

`y-7=\frac{6-7}{-2-4}(x-4)`

`y-7=\frac{1}{6}(x-4)`

`6y-42=x-4`

`x-6y+38=0`

Answer 2

`y=1/6x+19/3`

Explanation:

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

`•color(white)(x)y=mx+c`

`"where m is the slope and c 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)=(4,7)" and "(x_2,y_2)=(-2,6)`

`m=(6-7)/(-2-4)=(-1)/(-6)=1/6`

`y=1/6x+clarrcolor(blue)"is the partial equation"`

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

`"using "(-2,6)" then"`

`6=-1/3+crArrc=6+1/3=19/3`

`y=1/6x+19/3larrcolor(red)"equation in slope-intercept form"`