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Algebra / Linear equations in two variables Difficulty: Easy

A line in the xy-plane has a slope of $\frac{1}{9}$ and passes through the point $left parenthesis 0 comma 14 right parenthesis$ . Which equation represents this line?

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Explanation

Choice D is correct. The equation of a line in the xy-plane can be written as $y = m x + b$ , where $m$ represents the slope of the line and $left parenthesis 0 comma b right parenthesis$ represents the y-intercept of the line. It's given that the slope of the line is $\frac{1}{9}$ . It follows that $m = \frac{1}{9}$ . It's also given that the line passes through the point $left parenthesis 0 comma 14 right parenthesis$ . It follows that $b equals 14$ . Substituting $\frac{1}{9}$ for $m$ and $14$ for $b$ in $y = m x + b$ yields $y = \frac{1}{9} x + 14$ . Thus, the equation $y = \frac{1}{9} x + 14$ represents this line.

Choice A is incorrect. This equation represents a line with a slope of $- \frac{1}{9}$ and a y-intercept of $left parenthesis 0 comma negative 14 right parenthesis$ .

Choice B is incorrect. This equation represents a line with a slope of $- \frac{1}{9}$ and a y-intercept of $left parenthesis 0 comma 14 right parenthesis$ .

Choice C is incorrect. This equation represents a line with a slope of $\frac{1}{9}$ and a y-intercept of $left parenthesis 0 comma negative 14 right parenthesis$ .