Question

How do I write an equation for the line passing through (-2,4) and (-3,3)?

Answer 1

`y=x+6`

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)"distance formula"`

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

`"let "(x_1,y_1)=(-2,4)" and "(x_2,y_2)=(-3,3)`

`rArrm=(3-4)/(-3-(-2))=(-1)/(-1)=1`

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

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

`"using "(-2,4)" then"`

`4=-2+brArrb=4+2=6`

`rArry=x+6larrcolor(red)"in slope-intercept form"`

Answer 2

y=1x+6

Explanation:

So here we'll use the formula y=kx+m which is a linear equation.
To get k we have to have to points and then take y1-y2/x1-x2, so let me show you with maths.

#(y1-y2)/(x1-x2)= (4-3)/(-2--3)= 1/1=1#

So now we know k = 1 so now we have `y=1*x+m`

And now we can put in on of the two points you gave us so either (-2,4) (-3,3). I personally put in (-3,3) just because.

so we get: `3=1*-3+m`

Now we can solve M

`3=1*-3+m`
`3=-3+m`
`6=m`

And now we have the entire formula which i:
`y=1*x+6`

You can double check my by putting in on of your points in the equation.

Hopes this helps!