Final answer:
To find the equation of the line, the slope is calculated first using the points, followed by finding the y-intercept. The correct slope-intercept form of the line is y = (2/3)x + 18, which is not listed in the given options.
Step-by-step explanation:
The student is asking for the slope-intercept form of the equation of a line that passes through two given points. To find this, we first need to calculate the slope of the line using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. After finding the slope, we use either of the two points to solve for the y-intercept of the line.
Step-by-step Solution:
- Calculate the slope (m): m = (30 - 12) / (18 - (-9)) = 18 / 27 = 2 / 3.
- Choose one of the points to plug into the slope-intercept form (y = mx + b) and solve for b (the y-intercept). For point (18, 30): 30 = (2 / 3) * 18 + b.
- Simplify and solve for b: b = 30 - 12 = 18.
- Write the final equation: y = (2 / 3)x + 18.
Therefore, none of the given options A, B, C, or D is correct. The actual slope-intercept form of the line that passes through the points (18,30) and (-9,12) is y = (2/3)x + 18.