Question

Use the equation below to answer the question.

y = 3x + 6
Which equivalent equation is correctly matched with a key feature of the graph of the function it represents?
A
y = 3(x + 2) highlights that the y-intercept is at -2.
y = 3(x + 2) highlights that the y-intercept is at 2.
© y = 3(x + 2) highlights that the x-intercept is at -2.
y = 3(x + 2) highlights that the x-intercept is at 2.

Answer 1

The equivalent equation is correctly matched with a key feature of the graph is

y = 3(x + 2) highlights that the x-intercept is at -2.

Explanation:

Given:

`y=3x+6`

Solution:

The Given Equation is in Slope - Point Form i.e

`y=mx+c`

Where,

`m=slope\\\\c=y-intercept`

On Comparing the given equation with above we get

`slope=m=3\\\\y-intercept =6`

Now we Know that

Intercepts:

The line which intersect on x-axis and y-axis are called intercepts.

There are two intercepts:

y-intercept: The line which intersect at y-axis. So when the line intersect at y-axis X coordinate is zero.

x-intercept: The line which intersect at x-axis. So when the line intersect at x-axis Y coordinate is zero.

For x-intercept

Put y = 0 in

`y=3(x+2)`

`0=3x+6\\\\3x=-6\\\\\therefore x=(-6)/(3)=-2`

∴ x-intercept of

`y=3x+6`

x-intercept = -2

The equivalent equation is correctly matched with a key feature of the graph is

y = 3(x + 2) highlights that the x-intercept is at -2.