Find the slope of a line parallel to the line whose equation is x - y = 8. Fully simplify your answer.
To find the slope of a line parallel to another line, we need to find the slope of the given line first.
Let's rearrange the equation x - y = 8 to slope-intercept form (y = mx + b), where m is the slope:
y = x - 8
Comparing this equation to the slope-intercept form, we can tell that the slope of the line is 1.
Since a parallel line has the same slope, the slope of a line parallel to x - y = 8 is also 1.
Find the slope of a line perpendicular to the line whose equation is 4x - 6y = -60. Fully simplify your answer.
To find the slope of a line perpendicular to another line, we need to find the slope of the given line first.
Let's rearrange the equation 4x - 6y = -60 to slope-intercept form (y = mx + b), where m is the slope:
-6y = -4x - 60
Dividing both sides by -6, we get:
y = (4/6)x + 10
Simplifying the equation, we have:
y = (2/3)x + 10
Comparing this equation to the slope-intercept form, we can tell that the slope of the line is 2/3.
To find the slope of a line perpendicular to this line, we can take the negative reciprocal of the given slope.
The negative reciprocal of 2/3 is -3/2.
Therefore, the slope of a line perpendicular to 4x - 6y = -60 is -3/2.
To find the slope of a line parallel to the given line, we need to determine the slope of the given line first. The equation of the given line is x - y = 8.
Let's rewrite this equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
x - y = 8
-y = -x + 8
y = x - 8
From this equation, we can see that the slope of the given line is 1, since the coefficient of x is 1.
Now, the slope of any line parallel to this line will also be 1, since parallel lines have the same slope.
Therefore, the slope of a line parallel to the line x - y = 8 is 1.
To find the slope of a line parallel to another line, we need to determine the slope of the given line.
The given line equation is x - y = 8. To determine the slope, we need to rewrite the equation in slope-intercept form, which is given by y = mx + b, where m represents the slope.
Let's rearrange the given equation to get it in the slope-intercept form:
x - y = 8
We need to isolate y, so let's subtract x from both sides:
-y = -x + 8
Since we want y to be positive, we can multiply both sides of the equation by -1 to change the signs:
y = x - 8
Now we can see that the slope of the given line is 1, since the coefficient of x is 1.
A line parallel to the given line will have the same slope. Therefore, the slope of a line parallel to x - y = 8 is also 1.
So, the fully simplified answer is that the slope of a line parallel to the line x - y = 8 is 1.