Interpret the equation y=−4x+10

Question

. What type of function does this equation define? Describe its graph.

options:

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 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 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.

Answer 1

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

• The slope (m) is \(-4\), which indicates that for every unit increase in \( x \), \( y \) decreases by 4 units.
• The y-intercept (b) is \( 10 \), meaning that the graph intersects the y-axis at the point \( (0, 10) \).

The graph of this function is a straight line that slopes downward from left to right.

Considering the options provided, 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.

Answer 2

The equation of a function is y=2x−6
. If this function were graphed, what would its y
-intercept be?

Answer 3

To find the y-intercept of the equation \( y = 2x - 6 \), we set \( x = 0 \) and solve for \( y \).

Substituting \( x = 0 \) into the equation:

\[ y = 2(0) - 6 \] \[ y = -6 \]

Thus, the y-intercept of the function \( y = 2x - 6 \) is \( -6 \), which indicates that the graph intersects the y-axis at the point \( (0, -6) \).

Answer 4

What can you interpret about the equation y=−2x−8
?

options:

The slope is 2, the y
-intercept is −8
, and the line is rising from left to right.
The slope is 2, the y -intercept is negative 8 , and the line is rising from left to right.

The slope is −2
, the y
-intercept is 8, and the line is rising from left to right.
The slope is negative 2 , the y -intercept is 8, and the line is rising from left to right.

The slope is −2
, the y
-intercept is 8, and the line is falling from left to right.
The slope is negative 2 , the y -intercept is 8, and the line is falling from left to right.

The slope is −2
, the y
-intercept is −8
, and the line is falling from left to right.

Answer 5

To interpret the equation \( y = -2x - 8 \):

1. Slope: The coefficient of \( x \) is \(-2\), which means the slope \( m = -2 \). This indicates that the line falls (decreases) as you move from left to right.

2. Y-Intercept: The constant term is \(-8\). This means the y-intercept \( b = -8 \). Thus, the graph intersects the y-axis at the point \( (0, -8) \).

Based on this analysis, the correct interpretation from the given options is:

The slope is -2, the y-intercept is -8, and the line is falling from left to right.