Interpret the equation y=−4x+10

Question

. 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 has a maximum at (0,10)
.
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 slope of −4 and a y-intercept of 10.

Answer 1

The equation \( y = -4x + 10 \) defines a linear function.

To interpret it:

• Slope: The slope of the line is \(-4\), which means that for every unit increase in \( x \), the value of \( y \) decreases by 4 units. This indicates that the line is descending from left to right.

• Y-intercept: The y-intercept is \( 10 \), which means the line crosses the y-axis at the point \((0, 10)\).

Graphically, this function will be represented by a straight line that slopes downward from left to right, starting from the y-intercept at (0, 10).

Given the responses, the correct interpretation is:

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