Write the equation of the line in fully simplified slope-intercept form.
(9,3), (6,4)
To find the equation of the line, we first need to find the slope (m) of the line using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the coordinates (9,3) and (6,4), we have:
m = (4 - 3) / (6 - 9)
m = 1 / (-3)
m = -1/3
Next, we substitute the slope and one of the given points (6,4) into the slope-intercept form (y = mx + b) and solve for the y-intercept (b).
4 = (-1/3)(6) + b
4 = -2/3 + b
b = 4 + 2/3
b = 12/3 + 2/3
b = 14/3
Finally, we substitute the slope (-1/3) and y-intercept (14/3) into the slope-intercept form to obtain the equation of the line:
y = (-1/3)x + 14/3
To find the equation of the line in slope-intercept form (y = mx + b), we need to find the slope (m) and the y-intercept (b).
Step 1: Calculate the slope (m)
The formula for calculating the slope (m) is:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (9,3) and (6,4):
m = (4 - 3) / (6 - 9)
m = 1 / (-3)
m = -1/3
Step 2: Determine the y-intercept (b)
To determine the y-intercept, we can substitute the slope (m) and any of the given points (x, y) into the slope-intercept form and solve for b.
Using the point (9,3):
3 = (-1/3) * 9 + b
3 = -3 + b
b = 3 + 3
b = 6
Step 3: Write the equation in slope-intercept form
With the slope (m) and y-intercept (b) determined, the equation of the line in slope-intercept form is:
y = -1/3x + 6
To find the equation of the line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b).
The slope (m) can be calculated using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Given that the coordinates of two points on the line are (9,3) and (6,4), we can substitute these values into the slope formula:
m = (4 - 3) / (6 - 9)
m = 1 / (-3)
m = -1/3
Now that we have the slope (m), we can use one of the given points to solve for the y-intercept (b). Let's use the point (9,3):
y = mx + b
3 = (-1/3)(9) + b
We can simplify this equation by multiplying -1/3 and 9:
3 = -3 + b
To solve for b, we add 3 to both sides of the equation:
3 + 3 = b
6 = b
Now we have both the slope (m = -1/3) and the y-intercept (b = 6). Incorporating these values into the equation, we get the fully simplified slope-intercept form:
y = (-1/3)x + 6