Question

The function f is defined by f (x) = 3x + 10. What is the slope of the graph of y = f (x) in the xy-
plane
2
7​

Answer 1

Given:

The function:

$f (x) = 3x + 10$

To find:

The slope of the given graph in xy plane = ?

Solution:

Given that: $f (x) = 3x + 10$

OR

$y = f (x)\\\Rightarrow y = 3x + 10$

Please have a look at the attached image for the graph of equation:$y = 3x + 10$ ...... (1)

The equation of a line is given as:

$y=mx+c$ ...... (2)

Where $(x,y)$ is the coordinate of points that satisfy the equation of line.

$m$ is the slope of line given by the formula:

$m = \dfrac{y_2-y_1}{x_2-x_1}$

Where $(x_1,y_1)$ and $(x_2,y_2)$ are any two points on the given equation of line.

$c$ is the y-intercept i.e. the value of $y$ where $x$ = 0.

Now, comparing the equations (1) and (2):

We get the value of $m$ and $y$ as:

$m= 3\\y=10$

$\therefore$ the slope of given line is 3.