Question

Determine which Linear Function represents the Line that extends through the given Coordinates:

s(0) = 4 and s(1) = -4.

Answer 1

The equation of the linear function that goes through the points (0, 4) and (1, -4) is y = -8x + 4.

Step-by-step explanation:

The student is looking for the equation of a linear function that passes through the points (0, 4) and (1, -4). To find the equation of the line, we need to use these points to determine the slope (m) and y-intercept (b) in the equation of the line, which is generally expressed as y = mx + b.

Finding the slope, we take the difference in y-coordinates divided by the difference in x-coordinates: m = (y2 - y1) / (x2 - x1) = (-4 - 4) / (1 - 0) = -8. The slope of the line is therefore -8.

Since the line passes through the point (0, 4), the y-intercept is 4. Hence, the equation of the line using the slope-intercept form is y = -8x + 4.