how do I solve the equation of the line
The scatter plot diagram shows the best fit line drawn from (18, 0) to (0, 12). Two dots are marked on the line at (3, 10), (12, 4) and the remaining dots are marked near the line.
A. y=-2/3x+12
B. y=-2/3x+18
C. y=-3/2x+12
D. y=-3/2x+18
To solve the equation of the line, we first need to find the slope of the line. The slope is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (18, 0) and (0, 12), we can substitute the values into the equation:
m = (12 - 0) / (0 - 18)
m = 12 / -18
m = -2/3
Now that we have the slope, we can use the point-slope form of the equation to find the y-intercept (b) of the line. The point-slope form is given by:
y - y1 = m(x - x1)
Using the point (3, 10), we can substitute the values into the equation:
y - 10 = (-2/3)(x - 3)
Next, we distribute the -2/3 to the terms in the parenthesis:
y - 10 = (-2/3)x + 2
Finally, we isolate the y variable by adding 10 to both sides:
y = (-2/3)x + 2 + 10
y = (-2/3)x + 12
Therefore, the equation of the line is y = -2/3x + 12. Option A.