Question

HELP

Which equation does the graph below represent? (1 point)

A coordinate grid is shown. The x-axis values are from negative 5 to positive 5 in increments of 1 for each grid line, and the y-axis values are from negative 15 to positive 15 in increments of 3 for each grid line. A line is shown passing through the ordered pairs negative 4, 12 and 0, 0 and 4, negative 12.
Question 5 options:

1)

y = fraction negative 1 over 3x

2)

y = −3x

3)

y = 3x

4)

y = fraction 1 over 3x

Answer 1

3) y = 3x

Explanation:

a line equation is typically written as

y = ax + b

a is the slope, the inclination of the line. it is defined as ratio of "y coordinate change / x coordinate change" when going from one point to another on the line.

so, e.g. going from (0,0) to (4,12) means

x changes by +4 (from 0 to 4)

y changes by +12 (from 0 to 12)

so, the slope is +12/+4 = 3

and the line equation starts like this

y = 3x + b

now, b is the y-intercept : the y value, where the line intercepts (crosses) the y-axis. in other words, the y value where x = 0.

and we have that right away, as the line goes through (0,0). that IS the y-intercept point. the y value there is 0.

therefore, b=0.

and so the full line equation is

y = 3x