Question

A proportional relationship is shown in the table below: what is the slope and what numbers do i graph. ty besties

Answer 1

The slope of the line is 3/5 and the equation of the line is y = 3/5x.

The slope of a line is a measure of its steepness, defined as the ratio of the vertical change (rise) to the horizontal change (run). For the given line with a slope of 3/5, this means that for every 5 units the line moves to the right (run), it also rises by 3 units. Mathematically, the slope (m) is expressed as m = Δy/Δx, where Δy is the change in y and Δx is the change in x.

The equation of the line, y = 3/5x, is in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. In this case, the slope (m) is 3/5, and there is no y-intercept offset (b is 0). This means that the line passes through the origin (0,0) on the coordinate plane.

To visualize, if you plot points on the line, you'll find that as x increases by 5 units, y increases by 3 units. The line extends infinitely in both directions, maintaining a consistent slope of 3/5.

Answer 2

The slope of the line is
`m = (3)/(5)` and the equation of the line is
`y = (3)/(5)\cdot x`.

Explanation:

From table we understand that slope of the line is constant, that is, for each change of
`x` there is one and only change in
`y`, fulfilling the main characteristic of a line and we can determine the slope for every point of the line by means of the following expression:

`m = (y_(f)-y_(o))/(x_(f)-x_(o))` (1)

Where:

`x_(o), x_(f)` - Initial and final x-coordinates of the line.

`y_(o), y_(f)` - Initial and final y-coordinates of the line.

If we know that
`(x_(o), y_(o)) = (0,0)` and
`(x_(f),y_(f)) = (8,4.8)`, then the slope of the line is:

`m = (4.8-0)/(8-0)`

`m = (3)/(5)`

From graph we conclude that x-intercept of the line is
`b = 0`. Hence, the equation of the line is
`y = (3)/(5)\cdot x` and we proceed to plot the expression with the help of a graphing tool.