Question

nterpret the equation y=−4x+10 . 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 is a curve. This is a nonlinear function. Its graph is a curve. 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 linear function. Its graph is a straight line with a slope of −4 and a y -intercept of 10.

Answer 1

The equation \( y = -4x + 10 \) defines a **linear function**. Here's the breakdown of its components:

- **Type of function**: Linear function
- **Graph**: The graph of this function is a straight line.
- **Slope**: The slope is -4, which means that for every increase of 1 unit in \( x \), \( y \) decreases by 4 units. This indicates the line descends as you move from left to right.
- **Y-intercept**: The y-intercept is 10, meaning the line crosses the y-axis at the point (0, 10).

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