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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 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. 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) ..

5 answers

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.

Explanation:

  • Type of Function: The equation is in the form \( y = mx + b \), where \( m \) represents the slope and \( b \) represents the y-intercept. Since it follows this linear form, it is classified as a linear function.
  • Slope: The slope is -4, indicating that for each increase of 1 unit in \( x \), the value of \( y \) decreases by 4 units. This means the line descends as it moves from left to right.
  • Y-intercept: The y-intercept is 10, which indicates that the line crosses the y-axis at the point (0, 10).

Graph:

  • This function's graph will be a straight line that starts at (0, 10) and moves downward due to the negative slope of -4. As \( x \) increases, \( y \) decreases, making the line slant downwards.

Therefore, the first option correctly describes the function and its graph.

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 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. 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) .

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.

Explanation:

  1. Type of Function: The equation is in slope-intercept form \( y = mx + b \), where:

    • \( m \) is the slope
    • \( b \) is the y-intercept

    Since it is in this form, it defines a linear function.

  2. Slope: The slope \( -4 \) indicates that as \( x \) increases by 1, \( y \) decreases by 4. This results in a descending line from left to right.

  3. Y-intercept: The y-intercept is \( 10 \), meaning that when \( x = 0 \), \( y \) equals \( 10 \). This is the point where the line crosses the y-axis, specifically at (0, 10).

Graph:

  • The graph will be a straight line starting at (0, 10) and inclined downward at a rate of 4 units in the \( y \) direction for every 1 unit increase in \( x \).

Incorrect Options:

  • The options discussing nonlinear functions or incorrect slope and intercept values are not consistent with the equation provided. Thus, they do not accurately represent the equation \( y = -4x + 10 \).

Conclusion:

The first option accurately describes the function's nature and its graphical representation.

pickj one

The correct choice is:

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