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

2 Answers
Apr 10, 2018

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"

Apr 10, 2018

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!