(6,1), (3,3), (0,5) what is the equation of the line in slope intercept form
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).
First, let's calculate the slope (m) using the formula:
m = (y₂ - y₁)/(x₂ - x₁)
Using the points (6,1) and (3,3):
m = (3 - 1)/(3 - 6)
m = 2/-3
Now, we have the slope (m) as -2/3.
To find the y-intercept (b), we can use any of the given points. Let's use the point (3,3):
y = mx + b
3 = (-2/3)(3) + b
3 = -2 + b
b = 5
Therefore, the y-intercept is 5.
Now we can write the equation of the line in slope-intercept form:
y = (-2/3)x + 5
Hence, the equation of the line in slope-intercept form is:
y = (-2/3)x + 5.
To find the equation of the line in slope-intercept form, we first need to calculate the slope (m) using the given points. The slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Let's calculate the slope using the points (6,1) and (3,3):
m = (3 - 1) / (3 - 6)
m = 2 / (-3)
m = -2/3
Now that we have the slope (m), we can use any of the given points to find the y-intercept (b). Let's use the point (0,5) to find the y-intercept.
Using the slope-intercept form equation: y = mx + b
We plug in the values for m, x, and y:
5 = (-2/3) * 0 + b
5 = 0 + b
b = 5
Now we have the slope (m) and the y-intercept (b), so we can write the equation of the line in slope-intercept form:
y = -2/3x + 5
To find the equation of a line in slope-intercept form (y = mx + b), you need to determine the slope (m) and the y-intercept (b) using the given points (6,1), (3,3), and (0,5).
Step 1: Find the slope (m):
The formula for slope (m) is:
m = (y2 - y1) / (x2 - x1)
Using the points (6,1) and (3,3), let's substitute the coordinates into the formula:
m = (3 - 1) / (3 - 6)
= 2 / (-3)
= -2/3
Step 2: Find the y-intercept (b):
The y-intercept (b) is the value of y when x is equal to zero in the equation y = mx + b. We can use the point (0,5) to find b.
Substituting the coordinates of (0,5) into the equation:
5 = (-2/3) * 0 + b
5 = b
Step 3: Write the equation in slope-intercept form:
We now have the slope (m) and the y-intercept (b).
y = mx + b
y = -2/3x + 5
Thus, the equation of the line in slope-intercept form is y = -2/3x + 5.