Answer:
Step-by-step explanation:
To determine if the graph is correct for the equation
�
=
−
�
+
4
y=−x+4, let's analyze the equation and compare it with the graph.
The equation
�
=
−
�
+
4
y=−x+4 represents a linear function in slope-intercept form, where:
�
m is the slope, which is
−
1
−1,
�
b is the y-intercept, which is
4
4.
This means that the line has a slope of
−
1
−1 (indicating that it goes down as
�
x increases) and intersects the y-axis at
�
=
4
y=4.
Looking at the graph provided:
The y-intercept is indeed at
�
=
4
y=4, which matches the equation.
The slope of the line appears to be decreasing as
�
x increases, consistent with a slope of
−
1
−1 in the equation.
So, based on the analysis, yes, the graph appears to be correct for the equation
�
=
−
�
+
4
y=−x+4.
The equation y = -x + 4 is in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is -1 (the coefficient of x) and the y-intercept is 4.
2. The slope of -1 means that the line should have a negative slope, indicating that it decreases as you move from left to right on the graph.
3. The y-intercept of 4 indicates that the line should intersect the y-axis at y = 4.
By examining the graph provided, check if the line:
- Has a negative slope, decreasing as you move from left to right.
- Intersects the y-axis at y = 4.
If the graph follows these characteristics, then it is the correct graph of y = -x + 4. If it doesn't match these characteristics, then the graph may not represent the equation y = -x + 4 accurately.
