Question

a line passes through the origin and has a slope of 1/2. which of the following points does the line pass through? (0, ) (, 1) (1, 2) (2, 1) user: what is the slope of the line passing through (1, 2) and (3, 8)? slope = 1/7 slope = 1/3 slope = 3 slope = 7

Answer 1

#1 Passing point: (2,1)

#2 Slope = 3

Explanation:

#1

A line passes through the origin and has a slope of 1/2

Passing point (0,0) and Slope (m) = 1/2

Using Point Slope form:

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

`y-0=(1)/(2)(x-0)`

`y=(1)/(2)x`

Check Point: (2,1)

`1=(1)/(2)* 2\Rightarrow 1=1` TRUE

Hence, The passing point is (2,1)

#2

The slope of the line passing through (1, 2) and (3,8)

Formula:

`m=(y_2-y_1)/(x_2-x_1)`

`m=(8-2)/(3-1)`

`m=3`

Hence, The slope of line passing through two points is 3

Answer 2

General equation of the line
y = mx + c

m=1/2
so
y = (1/2)x + c
if it passes through origin (0,0)
0 = (1/2*0) + c
0 = 0 + c
c = 0

so the equation is
y = (1/2)x

if the x is equal to 2,
y is (1/2)*2 = 1

so the point will be
(2,1)