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 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 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.

Answer 1

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

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 is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. This confirms it is a linear function.
• Slope: The slope \( -4 \) indicates that for every unit increase in \( x \), \( y \) decreases by \(4\). This means the line is decreasing.
• Y-Intercept: The y-intercept \( 10 \) means 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."