Final answer:
The equation of the line passing through points (2,0) and (0,3) is found by first calculating the slope, which is -1.5, and then using point-slope form to derive the slope-intercept form of the line, resulting in the equation y = -1.5x + 3.
Step-by-step explanation:
To write the equation of the line that passes through the points (2,0) and (0,3), you first need to find the slope of the line. The slope (m) can be found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. For our points, this gives us:
m = (3 - 0) / (0 - 2) = 3 / -2 = -1.5
Next, we'll use the slope and one of the points to write the equation in point-slope form, which is y - y1 = m(x - x1). Using the point (2,0), the equation becomes:
y - 0 = -1.5(x - 2)
To convert this to the slope-intercept form, y = mx + b, you can distribute and simplify:
y = -1.5x + 3
The equation of the line that passes through the points (2,0) and (0,3) is y = -1.5x + 3.