Question

What is the equation of the function that is graphed as line a?

y = 4 x - 3
y = - 1/4 x + 3
y = 1/4x + 3
y = -4 x - 3

Answer 1

y = 4x - 3

Explanation:

y = mx + b

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

The slope is 4. If you start at the point (0,-3) and go up 4 units and then 1 unit to the right, you will be back on the line at point (2,4) The slope is the rise over the run. The rise is 4 and the run is 1. 4/1 = 4.

The slope (m) is 4.

The y-intercept is where the line crosses the y axis. It crosses at (0,-3)

The y-intercept (b) is -3

Plug 4 in for m and -3 in for b

y = mx + b

y = 4x -3

Answer 2

`y = 4x - 3`

Explanation:

we need to find out the equation of the function that is graphed. From the given graph we can see that the line passes through points (0,-3) and (2,5) . So we can find out the slope of the line as ,

`\implies m =(y_2-y_2)/(x_2-x_1)=\tan\theta\\`

`\implies m =(-3-5)/(0-2) \\`

`\implies m =(-8)/(-2) \\`

`\implies \mathfrak{ m = 4 }\\`

Now we may use point slope form of the line to find out the equation of the line as,

`\implies y - y_1 = m(x-x_1) \\`

`\implies y -(-3) = 4(x-0) \\`

`\implies y +3 = 4x\\`

`\implies \underline{\underline{ y = 4x -3}} \\`

And we are done!

-TσηγSтαяκ