Why is it not possible to write the equation of the line through (8,-5) and (-8,-9) in slope-intercept form??
It IS possible.
The slope is -4/-16 = 1/4
-5 = 8/4 + b
b = -7
y = (1/4)x -7
so it's not undefined?
No, it's not undefined. If the second point were (8,-9) it would be undefined, because the line through the points would be vertical.
thanks
To write the equation of a line in slope-intercept form (y = mx + b), we need to know both the slope (m) and the y-intercept (b). However, in this case, there is a misconception. It is indeed possible to write the equation of the line through the given points in slope-intercept form.
To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1),
where (x1, y1) and (x2, y2) are the coordinates of the two points on the line. Let's plug in the values:
m = (-9 - (-5)) / (-8 - 8)
= (-9 + 5) / (-16)
= -4 / -16
= 1 / 4.
Now that we have the slope (m = 1/4), we can use one of the given points to find the y-intercept (b) by substituting the values of (x, y) into the slope-intercept form and solving for b. Let's use the point (8, -5):
-5 = (1/4) * 8 + b
-5 = 2 + b
b = -5 - 2
b = -7.
Therefore, the equation of the line through the points (8, -5) and (-8, -9) in slope-intercept form is y = (1/4)x - 7.