Question

question 1 of 5
select the correct answer.
which graph represents the equation ( y - 6 = -(x - 4) )?

Explanation:

Step1: Identify the form of the equation

The given equation is \( y - 6=-(x - 4) \), which is in the point - slope form of a linear equation \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(4,6) \) and the slope \( m=- 1 \).

Step2: Analyze the slope and the point

A slope of \( - 1 \) means that for every 1 unit we move to the right (increase in \( x \) by 1), we move down 1 unit (decrease in \( y \) by 1). The line should pass through the point \( (4,6) \). We can also rewrite the equation in slope - intercept form (\( y=mx + b \)) to get a better idea.
Starting with \( y - 6=-(x - 4) \), we distribute the negative sign: \( y - 6=-x + 4 \). Then we add 6 to both sides: \( y=-x+4 + 6=-x + 10 \). So the y - intercept is \( (0,10) \) and the x - intercept (when \( y = 0 \)) is found by setting \( 0=-x + 10\), so \( x = 10 \), the x - intercept is \( (10,0) \).

To identify the correct graph, we can check which graph has a line passing through \( (4,6) \), \( (0,10) \) and \( (10,0) \) with a slope of \( - 1 \).

(Note: Since the actual graphs are not fully visible in the provided image, but the process to identify the correct graph is as above. If we assume that among the given options, the graph that has a line with slope - 1, passing through (4,6), (0,10) and (10,0) is the correct one. For example, if there are three graphs, say left, middle, right, and the middle graph has these properties, then the answer would be the middle graph.)

Answer:

(The answer depends on the actual graphs. For example, if the correct graph is the middle one among the given options, then the answer is "The Middle Graph". If the graphs are labeled with equations or points, we can use the above - derived points and slope to identify. Since the full graph options are not provided, but the method to find is as explained.)