Question

interpret the equation y=−4x+10 . What type of function does this equation define? Describe its graph.(1 point) Responses 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. 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 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 correct interpretation of the equation \( y = -4x + 10 \) is that it defines a linear function. The graph of this equation is a straight line.

Specifically, this line has:

• A slope of \(-4\), which means that for every unit increase in \( x \), the value of \( y \) decreases by 4 units (indicating a downward slope).
• A y-intercept of \(10\), meaning that the line crosses the y-axis at the point \( (0, 10) \).

Thus, the correct response is: "This is a linear function. Its graph is a straight line with a slope of -4 and a y-intercept of 10."