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 x + 5
3y = 1 x + 5 3
B
y = 1 x + 7
3y = 1 x + 7 3
C y = 3x + 15y = 3 x + 15
D y = 3x – 3
To find the equation of a line in slope-intercept form, we need to find the slope and the y-intercept.
First, we find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (-3, 6) and (9, 10), we have:
m = (10 - 6) / (9 - (-3))
m = 4 / 12
m = 1/3
So, the slope of the line is 1/3.
Next, we can use the slope-intercept form of the equation, which is:
y = mx + b
We can substitute one of the given points into this equation to find the y-intercept (b).
Using the point (-3, 6):
6 = (1/3)(-3) + b
6 = -1 + b
b = 6 + 1
b = 7
So, the y-intercept is 7.
Therefore, the equation of the line in slope-intercept form is:
y = (1/3)x + 7
Looking at the given options, the correct equation is:
B) y = 1x + 7