Line s passes through the points (3,4) and (2,1).line t passes through the point (4,2) and is parallel to line s. What is the equation for line t

y=3x-10

Step-by-step explanation:

first, we need to find the slope of line s, as that will determine the slope of line t

the formula for the slope calculated from 2 points is (y2-y1)/(x2-x1)

we can label the points for (3,4) and (2,1)

x1=3

y1=4

x2=2

y2=1

substitute into the formula:

m=(y2-y1)/(x2-x1)

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

m=-3/-1

m=3/1

m=3

the slope of line s is 3

as said above, parallel lines have the same slope, but different y intercepts.

that means that line t will have the same slope as line s (3).

typically, lines are written in the form y=mx+b, where m is the slope and b is the y intercept

here's what is line t so far:

y=3x+b

we need to find b

because the line passes through the point (4,2), we can use it to solve for b

plug 4 in as x and 2 as y

2=3(4)+b

2=12+b

-10=b

so that means that b is -10

therefore the equation for line t is y=3x-10

Hope this helps! Good luck on your assignment!