What is the equation in slope-intercept form of the line that passes through the points (2,11) and (-4,-28)?
What is the equation in slope-intercept form of the line that passes through the points (2,11) and (-4,-28)?
y= 2⁄13x- 2
y= 2⁄13x+ 139⁄13
y=13⁄2x-2
y=13⁄2x+ 139⁄13
To find the equation of a line in slope-intercept form, which is y = mx + b, we need to find the slope (m) and the y-intercept (b).
First, let's find the slope (m). The slope is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (2,11) and (-4,-28), we can substitute these values into the formula:
m = (-28 - 11) / (-4 - 2)
m = (-39) / (-6)
m = 13/2
So, the slope (m) is 13/2.
Next, we need to find the y-intercept (b). We can use one of the given points and substitute the values into the equation y = mx + b and solve for b.
Using the point (2,11):
11 = (13/2)(2) + b
11 = 13 + b
b = -2
So, the y-intercept (b) is -2.
Therefore, the equation in slope-intercept form is:
y = (13/2)x - 2
Hence, the correct equation in slope-intercept form of the line that passes through the points (2,11) and (-4,-28) is y = (13/2)x - 2.