algebra help: use point-slope form to write an equation of a line thru the given points: (4,3) and (-2,1)?

Question

HELP!

Answer 1

The equation of a straight line passing through two points (x1,y1) and (x2.y2) is given by the formula,(y-y1)/(y1-y2) = (x-x1)/(x1-x2)
Therefore,the required equation is(y-3)/(3-1)=(x-4)/(4+2)
=>(y-3)/2=(x-4)/6
=>2(x-4)=6(y-3) [after cross multiplication]
=>2x-8=6y-18
=>2x-6y-8+18=0
=>2x-6y+10=0
=>x-3y+5=0 [dividing all trms by 2]
Therefore the reqd. equation is x-3y+5=0

Answer 2

you will possibly first do upward push over run. upward push is the substitute in y and run is the substitute in x. to locate upward push, do y2-y1 (2-6) so the advance is -4. The run is x2-x1 (3- -a million) so the run is 4 then do upward push over run = -4/4 = a million, so the slope is -a million next you could desire to locate the y intercept via. Slope intercept variety is y=mx+b, so which you will possibly plug in between the coordinates for x and y to locate b, the y intercept. m is the slope, a million shall we use (3,2) 2=-a million*3+b 2=-3+b upload 3 to the two aspects b= 5 equation= -x+5=y Y=X-a million is the respond

Answer 3

First find the slope between the points:
m = (y2 - y1) / (x2 - x1)
m = (1 - 3) / (-2 - 4) = -2 / -6 = 1/3
Now pick EITHER point, and substitute for x1 and y1 in the equation
y - y1 = m(x - x1)
So ... y - 3 = 1/3(x - 4)
That IS the point/slope form of that line. If you need to simplify it or write another way, you'd distribute and simplify to do that.

Answer 4

First find slope, which is change in y over change in x

= (3 - 1)/(4 - -2) = 2/6 = 1/3

Then pick either point and plug it into the formula (which is
y - y1 = m(x - x1)

y - 1 = 1/3 (x + 2)

or

y - 3 = 1/3 (x - 4)

Answer 5

y= (1-3)/(-2-4)