What is the equation in slope-intercept form for a line that passes through the points (-3, 6) and (9, 10)?
Responses
A. y = 1/3x + 5
B. y = 1/3 x + 7
C. y = 3x + 15y = 3 x + 15
D, y = 3x – 3
To find the equation in slope-intercept form for a line that passes through two points, you can use the formula:
y = mx + b
where m is the slope and b is the y-intercept.
First, calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Using the given points (-3, 6) and (9, 10):
m = (10 - 6) / (9 - (-3))
m = 4 / 12
m = 1/3
Now that you have the slope, plug it into the equation:
y = (1/3)x + b
To find b, substitute either of the points into the equation. Let's use (-3, 6):
6 = (1/3)(-3) + b
6 = -1 + b
b = 7
Finally, substitute the slope (1/3) and the y-intercept (7) back into the equation:
y = 1/3x + 7
Therefore, the correct answer is B. y = 1/3x + 7.