Question

which of the following statements is true? the coordinates of the point where the line crosses the y - axis always have the form (0,y). the coordinates of the point where the line crosses the x - axis always have the form (0,y). a horizontal line has an undefined slope. a vertical line has a slope of 0.

Explanation:

Step1: Recall slope and coordinate - axis concepts

The slope of a horizontal line is 0 because for a horizontal line $y = c$ (constant), and using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, the $y$ - values are the same so $m = 0$. The slope of a vertical line is undefined because for a vertical line $x = k$ (constant), and in the slope formula the denominator $x_2 - x_1=0$, and division by zero is undefined.
When a line crosses the $y$ - axis, the $x$ - coordinate of the point of intersection is 0, so the coordinates of the $y$ - intercept are of the form $(0,y)$. When a line crosses the $x$ - axis, the $y$ - coordinate of the point of intersection is 0, so the coordinates of the $x$ - intercept are of the form $(x,0)$.

Step2: Analyze each statement

• A vertical line has an undefined slope, not a slope of 0.
• A horizontal line has a slope of 0, not an undefined slope.
• The coordinates of the point where the line crosses the $x$ - axis have the form $(x,0)$, not $(0,y)$.
• The coordinates of the point where the line crosses the $y$ - axis always have the form $(0,y)$.

Answer:

The coordinates of the point where the line crosses the $y$-axis always have the form $(0,y)$.