Question

3
the x - and y - intercepts of a line in the (x,y) coordinate plane are both positive. which of the following statements about the line must be true?
a. the slope of the line is positive
b. the slope of the line is negative
c. the slope of the line is zero
d. the slope of the line is undefined
e. the line passes through the point (0,0)

Explanation:

Step1: Recall the formula for slope

The slope \(m\) of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let the \(x -\)intercept be \((a,0)\) where \(a>0\) and the \(y -\)intercept be \((0,b)\) where \(b > 0\).

Step2: Calculate the slope

Using the two - intercept points \((a,0)\) and \((0,b)\), the slope \(m=\frac{b - 0}{0 - a}=\frac{b}{-a}\). Since \(a>0\) and \(b>0\), \(m=-\frac{b}{a}<0\).

Answer:

B. The slope of the line is negative