Examples with solutions for Linear Function y=mx+b: Converting between graphs and equations

Exercise #1

Choose the appropriate function for the number line 4.

XY1234

Video Solution

Step-by-Step Solution

To solve this problem, we need to determine the function that corresponds to the line labeled "4" on the number line.

The line labeled "4" is depicted in orange and appears to pass through the origin, indicating that the y-intercept is 0. Therefore, the equation has the form y=mx y = mx .

Upon examining this line, we observe that it is direct and passes through the origin at a 4545^\circ angle to both axes, suggesting that the slope m m is 1. This is to say, for each unit increase in x x , y y also increases by the same magnitude.

  • The equation thus simplifies to y=x y = x .

We next compare our result to the given function choices:

  • Choice A: y=x y = -x (Negative slope)
  • Choice B: y=x y = x (Positive slope of 1)
  • Choice C: y=6x y = 6x (Steeper positive slope)
  • Choice D: y=6x y = -6x (Steeper negative slope)

The line labeled "4" directly matches Choice B, y=x y = x , as both the direction and slope align with our observations.

Therefore, the function corresponding to the number line labeled "4" is y=x y = x .

Answer

y=x y=x

Exercise #2

Which function describes the line numbered 1?

XY1234

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Determine if the given line labeled '1' has a positive or negative slope.
  • Find out if the line passes through the origin, which implies the y-intercept, b=0 b = 0 .
  • Identify the function equation based on the observations.

Now, let's work through each step:
- Observation shows that line '1' in red goes through the origin (intersects at the point (0,0)), confirming that the y-intercept, b b , is zero.
- Given that this line descends from left to right, the slope m m is negative. Therefore, the most likely function representation given the described visual descent is y=x y = -x .

Thus, the function describing the line numbered '1' is y=x y = -x .

Answer

y=x y=-x

Exercise #3

Which function represents line 3?

XY1234

Video Solution

Answer

y=6x y=6x

Exercise #4

Which function describes the line numbered 2?

XY1234

Video Solution

Answer

y=6x y=-6x

Exercise #5

Which function corresponds to the line marked IV IV ?

XYIIIIIIIV4141

Video Solution

Answer

y=x+1 y=-x+1

Exercise #6

Which function corresponds to the line marked III \text{III} ?

XYIIIIIIIV4141

Video Solution

Answer

y=x+4 y=-x+4

Exercise #7

Which function corresponds to the line marked II \text{II} ?

XYIIIIIIIV4141

Video Solution

Answer

y=x1 y=x-1

Exercise #8

Which function corresponds to the line marked I \text{I} ?

XYIIIIIIIV4141

Video Solution

Answer

y=x+4 y=x+4