Look at the graph shown below: A coordinate plane graph is shown. A line passes through the y-axis at 3 and through the point 2 comma 4. Which equation best represents the line? (4 points) y = 3x + 1 over 2 y = 1 over 2 x − 3 y = 1 over 2 x + 3 y = 3x + 3

Step-by-step explanation:

The general equation for a line is y = mx + b

b is the y intercept.

That means that the general equation becomes

y = mx + 3

because one of the points is on the y axis.

The other point will give you the slope (m)

when x = 2

y = 4

4 = 2m + 3         Subtract 3 from both sides

4 - 3 = 2m          Combine

1 = 2m                Divide by 2

m = 1/2

Well as near as I can read it, the third choice is the answer.

y = 1/2 x + 3

option 1 is correct.

step-by-step explanation:

y varies inversely with x and constant of variation is 4

the equation will be:

y = k/x

where k =4 so,

y = 4/x

if we put values of x of option 1 in the above equation and find values of y

y = 4/-2 => y =-2

y = 4/-1 => y = -4

y = 4/1 => y = 4

y = 4/2 => y =2

so, all the values of x and y are correct.

if we put values of x given in other options and find value of y we cannot find whole table satisfying the equation.

hence option 1 is correct.

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.