Write the equation of the line in fully simplified slope-intercept form.
(-3,7), (-6,8)
To find the slope of the line passing through the points (-3,7) and (-6,8), we use the formula:
slope (m) = (y2 - y1) / (x2 - x1)
Plugging in the coordinates, we have:
slope (m) = (8 - 7) / (-6 - (-3))
slope (m) = 1 / -3
Next, we can use the slope-intercept form of a linear equation, which is:
y = mx + b
where m is the slope and b is the y-intercept.
Let's substitute the slope (m) into the equation:
y = (-1/3)x + b
Now, to find b (the y-intercept), we can substitute the coordinates of one of the points into the equation. Let's use (-3,7):
7 = (-1/3)(-3) + b
7 = 1 + b
b = 7 - 1
b = 6
Finally, we can write the equation of the line in fully simplified slope-intercept form:
y = (-1/3)x + 6
To find the equation of the line in slope-intercept form, we need to determine the slope and the y-intercept.
Step 1: Find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Using the given points (-3,7) and (-6,8):
m = (8 - 7) / (-6 - (-3))
= 1 / (-3)
= -1/3
Step 2: Use the slope-intercept form of a line which is y = mx + b, where m is the slope and b is the y-intercept.
Substituting the point (-3,7):
7 = (-1/3)(-3) + b
7 = 1 + b
b = 7 - 1
b = 6
Therefore, the equation of the line in slope-intercept form is:
y = (-1/3)x + 6
To find the equation of the line in slope-intercept form, we need to determine the slope (m) and the y-intercept (b) of the line.
Step 1: Find the slope (m)
The formula to calculate the slope is:
m = (y2 - y1) / (x2 - x1)
Using the given points (-3,7) and (-6,8):
m = (8 - 7) / (-6 - (-3))
m = 1 / (-3)
m = -1/3
Step 2: Find the y-intercept (b)
The y-intercept is the point where the line crosses the y-axis. We can use either of the given points to find the y-intercept.
Using the point (-3,7), we have:
y = mx + b
7 = (-1/3)(-3) + b
7 = 1 + b
b = 7 - 1
b = 6
Step 3: Write the equation in slope-intercept form
Now that we have the slope (m) and the y-intercept (b), we can write the equation of the line in slope-intercept form:
y = mx + b
Therefore, the equation of the line is y = -1/3x + 6