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 = -12x + 1
y = -12x - 1
y = 12x + 1
y = -12x
The correct answer is: y = 12x + 1
To find the linear function that describes the given statement in the algebraic model, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Given that the function has a y-intercept of 1 (the point where the graph intersects the y-axis) and an x-intercept of -4 (the point where the graph intersects the x-axis), we can determine the slope and y-intercept values.
The y-intercept is the point (0, 1) since it lies on the y-axis. This means that when x=0, y=1. Therefore, the y-intercept value (b) is 1.
The x-intercept is the point (-4, 0) since it lies on the x-axis. This means that when y=0, x=-4. Therefore, the x-intercept value (-4) is the value where the function crosses the x-axis.
To calculate the slope (m), we can use the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points.
Using the points (0, 1) and (-4, 0), we have:
m = (0 - 1) / (-4 - 0) = -1 / -4 = 1/4
Now that we have determined the slope (1/4) and the y-intercept (1), we can write the linear function using the slope-intercept form:
y = (1/4)x + 1
Therefore, the linear function that describes the given statement in the algebraic model is y = (1/4)x + 1.