The equation of the line in slope-intercept form is y = -x + 3
The equation of the line in slope-intercept form is y = (1/3)x + 10/3
How to find the equations ?
Calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Let (x1, y1) = (2, 1) and (x2, y2) = (3, 0):
m = (0 - 1) / (3 - 2)
m = (-1) / (1)
m = -1
Use one of the given points (let's use (2, 1)) to find the y-intercept (b):
y = mx + b
1 = (-1)(2) + b
1 = -2 + b
b = 1 + 2
b = 3
The equation of the line in slope-intercept form is:
y = -x + 3
To write the equation of the line that passes through (-1, 3.5) and (0.5, 4):
m = (4 - 3.5) / (0.5 - (-1))
m = (0.5) / (0.5 + 1)
m = 0.5 / 1.5
m = 1/3
Find the y-intercept (b):
y = mx + b
3.5 = (1/3)(-1) + b
3.5 = (-1/3) + b
b = 3.5 + 1/3
b = (3.5*3/3) + 1/3
b = 10/3
The equation of the line in slope-intercept form is:
y = (1/3)x + 10/3