Question

A line has the given slope m and passes through the first point listed in the table. Complete the table so that each point on the table lies on the line.

Answer 1

A line can be written as an equation in the slope-intercept form:

`y=mx+b`

Where m is the slope and b is the y-intercept.

We know the slope:

`m=3`

The y-intercept is the y value of the graph where it intercepts the y-axis, which happens when x = 0.

We know that the point x = 0 and y = 3 is on the line and, since the value of x is 0. the y value is the y-interceot, so:

`b=3`

Thus, we have the equation:

`y=3x+3`

To calculate the other points, we just need to substitute their x values and get their y values:

x = 1:

`y=3\cdot1+3=3+3=6`

So, when x = 1, y = 6

x = 2:

`y=3\cdot2+3=6+3=9`

So, when x = 2, y = 9.

x = 3:

`y=3\cdot3+3=9+3=12`

So, when x = 3, y = 12;

So, the complete table is:

x | 0 | 1 | 2 | 3

y | 3 | 6 | 9 | 12