For the statement “Function has a y-intercept of 1 and x-intercept of -4”, find the linear function which describes the given statement in the algebraic model.
y = -1/2x + 1
y = -1/2x - 1
y = 1/2x + 1
y = -1/2x
None of the given options accurately describe the given statement.
The correct linear function that describes the given statement is:
y = -1/2x + 1
To find the linear function that describes the given statement, we need to consider the definition of y-intercept and x-intercept.
The y-intercept is the point where the graph of the function intersects the y-axis. It is the value of y when x equals zero. From the statement, we know that the function has a y-intercept of 1. This means that when x equals zero, y equals 1.
Therefore, the equation of the linear function includes the term +1.
Now let's consider the x-intercept. The x-intercept is the point where the graph of the function intersects the x-axis. It is the value of x when y equals zero. From the statement, we know that the function has an x-intercept of -4. This means that when y equals zero, x equals -4.
Therefore, the equation of the linear function includes the term -4.
Combining the information we have, the linear function that describes the given statement in the algebraic model is:
y = m*x + b,
where m is the slope of the function and b is the y-intercept.
From the statement, we know that the y-intercept is 1. Therefore, b = 1.
Now we need to determine the slope of the function. The slope is equal to the change in y divided by the change in x. We can use the information about the x-intercept and y-intercept to find the slope.
The change in y is from the y-intercept (0, 1) to the x-intercept (-4, 0). Therefore, the change in y is 0 - 1 = -1.
The change in x is from the x-intercept (-4, 0) to the y-intercept (0, 1). Therefore, the change in x is 0 - (-4) = 4.
Therefore, the slope of the function is -1/4.
Putting the values together, the linear function that describes the given statement in the algebraic model is:
y = -1/4 * x + 1
To find the linear function that describes the given statement, we need to determine the equation of the line. The statement tells us that the function has a y-intercept of 1 and an x-intercept of -4.
The y-intercept is the point at which the line intersects the y-axis, which occurs when x = 0. So, one point on the line is (0, 1).
The x-intercept is the point at which the line intersects the x-axis, which occurs when y = 0. So, another point on the line is (-4, 0).
Using the two points, we can find the slope of the line using the formula:
slope = (y2 - y1) / (x2 - x1)
Then, substitute the slope and one of the points into the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
Let's calculate the slope first:
slope = (0 - 1) / (-4 - 0) = -1 / -4 = 1/4
Now, substitute the slope and either of the given points:
y - 1 = (1/4)(x - 0)
Simplifying the equation:
y - 1 = 1/4x
To express the equation in the standard form, we can multiply through by 4 to eliminate the fraction:
4y - 4 = x
Rearranging the equation:
x - 4y + 4 = 0
So, the linear function that describes the given statement in the algebraic model is: x - 4y + 4 = 0