A. −4/3
B. 4/3
C. 3/4
D. −3/4
5 answers
To find the slope of a line given two points, we can use the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
In this case, we have the points (3, 0) and (0, -4). Let's assign:
Now, substitute the values into the slope formula:
\[ m = \frac{-4 - 0}{0 - 3} \]
This simplifies to:
\[ m = \frac{-4}{-3} = \frac{4}{3} \]
So the slope of the line is:
\[ \boxed{\frac{4}{3}} \]
Thus, the correct answer is B. \( \frac{4}{3} \).
To find the x- and y-intercepts of the equation \(3y - 2x = 18\), we can set \(y = 0\) to find the x-intercept, and set \(x = 0\) to find the y-intercept.
Finding the x-intercept:
Set \(y = 0\):
\[ 3(0) - 2x = 18 \]
This simplifies to:
\[ -2x = 18 \]
Now, solve for \(x\):
\[ x = \frac{18}{-2} = -9 \]
So the x-intercept is \((-9, 0)\).
Finding the y-intercept:
Set \(x = 0\):
\[ 3y - 2(0) = 18 \]
This simplifies to:
\[ 3y = 18 \]
Now, solve for \(y\):
\[ y = \frac{18}{3} = 6 \]
So the y-intercept is \((0, 6)\).
Summary:
The x-intercept is \((-9, 0)\) and the y-intercept is \((0, 6)\).
To find the x- and y-intercepts of the equation \(6y + 4x = 22\), we'll follow the method of setting one variable to zero to find the other.
Finding the x-intercept:
Set \(y = 0\):
\[ 6(0) + 4x = 22 \]
This simplifies to:
\[ 4x = 22 \]
Now, solve for \(x\):
\[ x = \frac{22}{4} = \frac{11}{2} = 5.5 \]
So the x-intercept is \(\left(\frac{11}{2}, 0\right)\) or \((5.5, 0)\).
Finding the y-intercept:
Set \(x = 0\):
\[ 6y + 4(0) = 22 \]
This simplifies to:
\[ 6y = 22 \]
Now, solve for \(y\):
\[ y = \frac{22}{6} = \frac{11}{3} \]
So the y-intercept is \(\left(0, \frac{11}{3}\right)\) or \((0, 3.67)\) (approximately).
Summary:
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