Question

What is an equation of the line that passes through the points (3,1) and (4,4)?

Answer 1

y=3x-8

Explanation:

find the slope by using the slope formula: y2-y1/x2-x1 so 4-1/4-3 solve 3/1 so the slope is 3. standard lines are y = mx+b plug it in with one of the points: 4= 4(3) + b the m is the slope and I plugged the x and y points 4 into it. 4=12+b subtract 12, b=-8 that is the y intercept.

check 1=3(3) + b, 1= 9 + b, -8= b:

so the y intercept is -8 the slope is 3 now we replace it to get a linear equation;

y=3x-8

Answer 2

The equation of the line that passes through the points (3,1) and (4,4) is (3x-y=8).

Explanation:

Given ;
`(x_1,y_1),(x_2,y_2)=(3,1) , (4,4)`

Equation of the line that passes through the points can be determined by using point slope form equation of line;

`(y-y_1)=m* (x-x_1)`

slope of the line = m

`m=(y_2-y_1)/(x_2-x_1)=(4-1)/(4-3)=(3)/(1)`

`(y-1)=3(x-3)`

`y-1=3x-9`

`3x-y=9-1`

`3x-y=8`

The equation of the line that passes through the points (3,1) and (4,4) is (3x-y=8).