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 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.
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.

Answer 1

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

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

Here's a brief explanation:

• Linear Function: The equation is in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. Since this is a linear equation, the graph will be a straight line.
• Slope: The slope is \(-4\), indicating that for each increase of \(1\) in \(x\), \(y\) decreases by \(4\).
• Y-intercept: The y-intercept is \(10\), which means the line crosses the y-axis at the point \((0, 10)\).

Thus, the graph will be a straight line that slopes downward from left to right, starting at the point \((0, 10)\).