Question

Identify the graphed linear equation.

A) y = 4x + 1
B) y = 4x - 1
C) y = -4x + 1
D) y = -4x - 1

Answer 1

C)
`y = -4x + 1`

Explanation:

Our most commonly used equation for a graphed line is slope intercept form, or
`y = kx + b`. In the slope intercept form, y is the y-coordinate, x is the x-coordinate, and most importantly, k is the slope and b is the y-intercept.

We calculate the slope by rise/run. The rise is the difference between the y-coordinate per length and the run is the difference between the x-coordinates per length.

For example,
`A(x_(1) ,y_(1))` and [tex]B(x_{2},y_{2})[tex] are the two points that are selected. And we calculate the differences.

The rise is the difference between the y-coordinates, so it will be [tex]y_{1} - y_{2}[tex]. The run is the difference between the x-coordinates, so it will be [tex]x_{1} - x_{2}[tex].

In the case of this graph, the two points I chose was (0,1) and (1,-3). So the rise is 1 - (-3) = 4. But this line is a line going downwards, so the slope has to be -4. The run, obviously, is 0 - 1 = -1, but all runs have to be positive, so the run is 1.

With the equation rise/run, the slope is [tex]-4 / 1 = -4[tex].

So the [tex]k[tex] in the equation, which is the slope, is -4.

The [tex]b[tex] in the equation is the y-intercept, or where the line crosses the y-axis. In this graph, the line crosses the y-axis at (0,1) and the y-coordinate is 1 so the y-intercept is also 1.

So the final answer is [tex]y = -4x + 1[tex].

Answer 2

C

Explanation:

It has a point at (0,1) which means that the graph starts there. ( +1 at the end of the equation.) Then the slope is going downwards, so you can tell it is a negative.