What is the equation in slope-intercept form for a line that passes through the points (-3, 6) and (9, 10)?
Responses
y =1/3x + 5
y = 1/3 x + 7
y = 3x + 15
y = 3x – 3
To find the equation in slope-intercept form, we first need to find the slope (m) and the y-intercept (b).
The slope (m) can be found 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 we have the slope, we can use the point-slope form of the equation for a line:
y - y1 = m(x - x1)
Let's choose the point (-3, 6) to substitute in the equation:
y - 6 = 1/3(x - (-3))
y - 6 = 1/3(x + 3)
To convert this equation into slope-intercept form (y = mx + b), we need to isolate y:
y - 6 = 1/3x + 1
y = 1/3x + 1 + 6
y = 1/3x + 7
Therefore, the equation in slope-intercept form for the line that passes through the points (-3, 6) and (9, 10) is:
y = 1/3x + 7.