Interpret the equation y=−4x+10

Question

. What type of function does this equation define? Describe its graph.(1 point)
Responses

This is a linear function. Its graph is a straight line with a y
-intercept of −4
and a slope of 10.
This is a linear function. Its graph is a straight line with a y -intercept of negative 4 and a slope of 10.

This is a nonlinear function. Its graph has a maximum at (0,10)
.
This is a nonlinear function. Its graph has a maximum at left parenthesis 0 comma 10 right parenthesis .

This is a nonlinear function. Its graph is a curve.
This is a nonlinear function. Its graph is a curve.

This is a linear function. Its graph is a straight line with a slope of −4
and a y
-intercept of 10.

Answer 1

The correct interpretation of the equation \( y = -4x + 10 \) is:

This is a linear function. Its graph is a straight line with a slope of -4 and a y-intercept of 10.

Explanation:

• Type of Function: The equation defines a linear function because it can be expressed in the standard form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
• Slope: The slope of the line is -4, which means that for every unit increase in \( x \), \( y \) decreases by 4 units.
• Y-Intercept: The y-intercept is 10, indicating that the line crosses the y-axis at the point (0, 10).

Graph Description:

The graph of this linear function is a straight line that slopes downward from left to right due to the negative slope. It will cross the y-axis at (0, 10) and will continue indefinitely in both directions.