What is the equation in slope-intercept form for a line that passes through the points (-3, 6) and (9, 10)? 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 of a line in slope-intercept form, we need to find the slope and y-intercept.
First, let's find the slope using the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the coordinates, (-3, 6) and (9, 10), we get:
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 point-slope form of a line to find the equation:
y - y1 = m(x - x1)
Plugging in the coordinates (-3, 6), we get:
y - 6 = (1/3)(x - (-3))
y - 6 = (1/3)(x + 3)
Now, let's simplify and rewrite the equation in slope-intercept form, y = mx + b:
y - 6 = (1/3)x + 1
y = (1/3)x + 1 + 6
y = (1/3)x + 7
Therefore, the equation in slope-intercept form is y = 1/3x + 7.
The answer is B) y = 1/3 x + 7.