The graph of the line with equation $ax + by = 1$ is shown above. Which of the following must be true?

Neetesh Kumar | October 19, 2024

College Algebra Homework Help

CLEPS College Algebra Guide Question 15
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Step-by-step solution:

We need to observe the given line's intercepts and slope to analyze it.

1. The line intersects the positive $x$-axis, meaning that when $y = 0$, $x > 0$.
   This implies that the $x$-intercept is positive, which suggests that $a > 0$.

2. The line intersects the positive $y$-axis, meaning that when $x = 0$, $y > 0$.
   This implies that the $y$-intercept is positive, which suggests that $b > 0$.

Thus, based on the intercepts of the line, the correct combination is $a > 0$ and $b < 0$.

Final Answer

• (Option - B) i.e. $a > 0$ and $b > 0$

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