Write an equation in slope intercept form of the line that passes through (4, 1) and (5, -1).
y-y1=m(x-x1)
-1-1=m(5-4)
M=-2
Olivia found the slope
so y = -2x + b
sub in one of the given points, I will use (4,1)
1 = -2(4) + b
b = 9
y = -2x + 9
(test it with the other point, it works)
To find the equation of a line in slope-intercept form (y = mx + b), you need to determine the values of m (slope) and b (y-intercept).
First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (4, 1) and (5, -1), we have:
m = (-1 - 1) / (5 - 4)
m = -2 / 1
m = -2
Now that we have the slope (m = -2), we can use any of the given points (4, 1) to find the y-intercept (b). We'll use the point (4, 1) and substitute the values into the slope-intercept form:
1 = -2(4) + b
1 = -8 + b
Adding 8 to both sides:
1 + 8 = -8 + b + 8
9 = b
Therefore, the y-intercept (b) is 9.
Now we have the slope (m = -2) and the y-intercept (b = 9), so we can write the equation of the line in slope-intercept form:
y = -2x + 9
Hence, the equation in slope-intercept form of the line passing through the points (4, 1) and (5, -1) is y = -2x + 9.