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

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 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)
.

Answer 1

The equation \( y = -4x + 10 \) defines a linear function. Its graph is a straight line with a slope of -4 and a y-intercept of 10.

Specifically, the slope of -4 indicates that for every one unit increase in \( x \), the value of \( y \) decreases by 4 units. The y-intercept of 10 means that the graph crosses the y-axis at the point (0, 10).

Thus, the correct interpretation from the provided responses is:

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