Answer :

Answer:

To find the linear function that describes the statement "Function has a y-intercept of 1 and x-intercept of -4", we can use the intercept form of a linear equation.

1. **Y-intercept**: The y-intercept is where the function crosses the y-axis. It is given as 1. So, the point (0, 1) lies on the function.

2. **X-intercept**: The x-intercept is where the function crosses the x-axis. It is given as -4. So, the point (-4, 0) lies on the function.

In general, a linear function in intercept form can be written as:

\[ y = mx + c \]

where \( c \) is the y-intercept and \( m \) is the slope of the line.

From the given points:

- The y-intercept \( c = 1 \)

- The x-intercept provides another point (-4, 0).

To find the slope \( m \):

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 1}{-4 - 0} = \frac{-1}{-4} = \frac{1}{4} \]

Now substitute the slope and y-intercept into the equation:

\[ y = \frac{1}{4}x + 1 \]

Therefore, the linear function that describes the given statement "Function has a y-intercept of 1 and x-intercept of -4" is \( y = \frac{1}{4}x + 1 \).

Answer:

[tex]y=\dfrac{1}{4}x+1[/tex]

Step-by-step explanation:

Features of a Linear Function

The equation of a linear function is

                                                y = mx + b,

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

[tex]\dotfill[/tex]

Slope

The slope or rate of change can be calculated by using two points on the function's graph and using the slope formula.

                                           [tex]slope=\dfrac{y_2-y_1}{x_2-x_1}[/tex],

where the subscripts indicate which coordinate point the value originates from.

[tex]\dotfill[/tex]

Intercepts

For y-intercepts, the x value is always 0. This makes sense since all y-intercepts are directly on the y-axis.

Similarly, x-intercepts have y-values of 0.

[tex]\hrulefill[/tex]

Solving the Problem

The problem tells us that the y-intercept is 1, so b = 1.

                                          y = mx + 1.

They also tell us that the x-intercept is -4, meaning

                                        0 = m(-4) + 1.

We need to find m to find the full equation of the function described.

Intercepts are also points on the graph, so we can write the x and y intercepts as (0,1) and (-4,0).

Now, we can plug them into the slope formula to find m!

                           [tex]slope=\dfrac{1-0}{0-(-4)} =\dfrac{1}{4}[/tex]

So, our equation for this function is

                                           [tex]y=\dfrac{1}{4}x+1[/tex].