Linear function y=mx+b - Examples, Exercises and Solutions

The linear function y=mx+by=mx+b actually represents a graph of a straight line that has a point of intersection with the vertical Y Y axis.

m m represents the slope.
When m m is positive, the slope is positive: the line goes upwards.
When m m is negative, the slope is negative: the line goes downwards.
When m=0 m = 0 , the slope is zero: the line is parallel to the X X axis.

b b represents the point where the line intersects the Y Y axis.
If b=0 b=0 , then the line will pass through the origin of the coordinates, that is, the point (0,0) \left(0,0\right)

La función lineal

Practice Linear function y=mx+b

Exercise #1

Calculate the slope of the line that passes through the points (4,1),(2,5) (4,1),(2,5) .

Video Solution

Step-by-Step Solution

Remember the formula for calculating a slope using points:

Now, replace the data in the formula with our own:

(51)(24)=42=2 \frac{(5-1)}{(2-4)}=\frac{4}{-2}=-2

Answer

-2

Exercise #2

What is the slope of a straight line that passes through the points (0,0),(8,2) (0,0),(-8,2) ?

Video Solution

Step-by-Step Solution

To solve the problem, remember the formula to find the slope using two points

 

Now, we replace the given points in the calculation:

 (02)(0(8)=28=14 \frac{(0-2)}{(0-(-8)}=\frac{-2}{8}=-\frac{1}{4}

Answer

14 -\frac{1}{4}

Exercise #3

Choose the correct answer for the function.

y=x+1 y=-x+1

Video Solution

Step-by-Step Solution

Let's start with option A

In a linear function, to check if the functions are parallel, you must verify if their slope is the same.

y = ax+b

The slope is a

In the original formula:

 y = -x+1

The slope is 1

In option A there is no a at all, which means it equals 1, which means the slope is not the same and the option is incorrect.

 

Option B:

To check if the function passes through the points, we will try to place them in the function:

-1 = -(-2)+1

-1 = 2+1

-1 = 3

The points do not match, and therefore the function does not pass through this point.

 

Option C:

We rearrange the function, in a way that is more convenient:

y = -1-x

y = -x-1

You can see that the slope in the function is the same as we found for the original function (-1), so this is the solution!

 

Option D:

When the slope is negative, the function is decreasing, as the slope is -1, the function is negative and this answer is incorrect.

Answer

The graph is parallel to the graph of function

y=1x y=-1-x

Exercise #4

For the function in front of you, the slope is?

XY

Video Solution

Answer

Negative slope

Exercise #5

For the function in front of you, the slope is?

XY

Video Solution

Answer

Negative slope

Exercise #1

For the function in front of you, the slope is?

XY

Video Solution

Answer

Negative slope

Exercise #2

For the function in front of you, the slope is?

XY

Video Solution

Answer

Negative slope

Exercise #3

For the function in front of you, the slope is?

XY

Video Solution

Answer

Negative slope

Exercise #4

For the function in front of you, the slope is?

XY

Video Solution

Answer

Negative slope

Exercise #5

For the function in front of you, the slope is?

XY

Video Solution

Answer

Positive slope

Exercise #1

For the function in front of you, the slope is?

XY

Video Solution

Answer

Positive slope

Exercise #2

For the function in front of you, the slope is?

XY

Video Solution

Answer

Positive slope

Exercise #3

For the function in front of you, the slope is?

XY

Video Solution

Answer

Positive slope

Exercise #4

Given the linear function:

y=x4 y=x-4

What is the rate of change of the function?

Video Solution

Answer

m=1 m=1

Exercise #5

Given the linear function:

y=14x y=1-4x

What is the rate of change of the function?

Video Solution

Answer

m=4 m=-4

Topics learned in later sections

  1. Function
  2. Linear Function
  3. Positive and Negativity of a Linear Function
  4. Slope in the Function y=mx
  5. Finding a Linear Equation
  6. Graphical Representation of a Function that Represents Direct Proportionality
  7. Representation of Phenomena Using Linear Functions