Question

A new graph is formed from y = 5x by changing the slope to 9 and y-intercept to 8. Which statement about the new relationship is true?

The new graph has a steeper slope and a y-intercept of 13.

The new graph has a steeper slope and y-intercept of 8.

The new graph has a less steep slope and a y-intercept of 13

The new graph has a less steep slope and a y-intercept of 8

Answer 1

The new graph has a steeper slope and a y-intercept of 8.

Explanation:

From Analytical Geometry, we define a straight line by following first order polynomial (linear function):

`y = m\cdot x + b` (1)

Where:

`x` - Independent variable.

`y` - Dependent variable.

`b` - y-Intercept.

`m` - Slope.

And the slope represents the change in dependent variable (
`\Delta y`) divided by the change in independent variable (
`\Delta x`). That is:

`m = (\Delta y)/(\Delta x)`

If
`m_(1) > 0` and
`m_(2) > m_(1)`, then the new line is steeper with respect to the original line.

Let
`y = 5\cdot x`, its slope and y-intercept are 5 and 0, respectively. If slope is changed into 9 and y-intercept becomes 8, then the new graph has a steeper slope and a y-intercept of 8.