Write an equation in slope-intercept form for the line through two points.
1. (7,8) and (-7, 6)
2. (-1, 2) and (4, -23)
Using y = mx + b, first we need the slope m
m = (8-6)/(7-(-7))
= 2/14 = 1/7
sofar: y = (1/7)x + b
sub in (7,8)
8 = (1/7)(7) + b
8 = 1 + b
7 = b
y = (1/7)x + 7
I usually check, by testing with the point that was not used in the substitution , in this case (-7,6)
LS = 6
RS = (1/7)(-7) + 7
= -1 + 7
= 6
= LS
My equation is correct.
Do the 2nd problem the same way, let me know what you get.
2. When I was attempting to find the slope, I received 2/22 as the fraction. However, I do not know nor remember how to reduce it.
look for a number which divides into both of them, in this case 2
2/22 = 1/11
HOWEVER, how did you ever get 2/22 ?
Remember, you have to start with the y's on top and the x's in the denominator
slope = (2 - (-23))/(-1-4)
= 25/-5
= -5
so y = 5x + b
using (-1,2)
2 = -5(-1) + b
2 = 5 + b
-3 = b
y =-5x - 3
does (4, -23) satisfy this??
2)
(-1,2 ) and (4,-23)
m = (-23-2)/(4-(-1) = -25/5
m = -5
y = mx + b
2 = (-5)(-1) + b
2 = 5 + b
2-5 = 5-5 + b
-3 = b
y = mx + b
y = -5x -3
To find the equation of a line in slope-intercept form (y = mx + b), you need two points on the line. Let's solve both examples one by one:
1. (7,8) and (-7,6):
First, we need to find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the points.
Using the given points, we can substitute the values:
m = (6 - 8) / (-7 - 7)
m = -2 / -14
m = 1/7
Now that we have the slope (m), we can substitute it into the slope-intercept form equation (y = mx + b) with one of the points (x, y) to find the y-intercept (b).
Using the point (7,8):
8 = (1/7)(7) + b
8 = 1 + b
b = 8 - 1
b = 7
The equation of the line through the points (7,8) and (-7,6) in slope-intercept form is:
y = (1/7)x + 7
2. (-1,2) and (4,-23):
Similarly, we'll find the slope (m) first:
m = (-23 - 2) / (4 - (-1))
m = -25 / 5
m = -5
Now, substitute the slope (m) into the slope-intercept form equation (y = mx + b) using one of the points (x, y) to find the y-intercept (b).
Using the point (-1,2):
2 = (-5)(-1) + b
2 = 5 + b
b = 2 - 5
b = -3
The equation of the line through the points (-1,2) and (4,-23) in slope-intercept form is:
y = -5x - 3