Question

match the form or formula with its name.
y=k
horizontal line
standard form
slope formula
vertical line
slope-intercept form
point-slope formula

Explanation:

To determine the name of the formula \( y = k \), we analyze the characteristics of each option:

• A horizontal line has the equation \( y = k \), where \( k \) is a constant. This means for all \( x \)-values, the \( y \)-value remains \( k \), creating a horizontal line.
• Standard form is typically \( Ax + By = C \) (where \( A \), \( B \), \( C \) are constants and \( A,B \) not both zero), so \( y = k \) is not standard form.
• The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \), which is for calculating slope, not matching \( y = k \).
• A vertical line has the equation \( x = k \), not \( y = k \).
• Slope - intercept form is \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. In \( y = k \), the slope \( m = 0\) and \( b=k \), but the specific name for \( y = k \) (when slope is 0) is a horizontal line, and "slope - intercept form" is a more general form that includes cases with non - zero slope.
• Point - slope formula is \( y - y_1=m(x - x_1) \), which is not \( y = k \).

So the formula \( y = k \) matches the "Horizontal line" option.

Answer:

Horizontal line