Final answer:
The slope-intercept form of the linear function that passes through the points (-1.5, 0) and (0, -3) is y = -2x - 3, with a slope of -2 and a y-intercept of -3.
Step-by-step explanation:
To find the slope-intercept form of the linear function given two points (-1.5, 0) and (0, -3), we first need to calculate the slope (m) of the line. The slope (m) is defined as the rise over the run, which can be determined using the formula m = (y2 - y1) / (x2 - x1). Applying this formula:
m = (-3 - 0) / (0 - (-1.5)) = -3 / 1.5 = -2
Now that we know the slope, we can use one of the given points to find the y-intercept (b). Since the point (0, -3) is where the line crosses the y-axis, -3 is the y-intercept.
With the slope m = -2 and y-intercept b = -3, the slope-intercept form of the equation is y = mx + b, which simplifies to:
y = -2x - 3