graph $y = -\frac{1}{4}x + 6$.

Explanation:

Step1: Identify the slope-intercept form

The equation ( y = -\frac{1}{4}x + 6 ) is in slope - intercept form ( y=mx + b ), where ( m=-\frac{1}{4} ) (slope) and ( b = 6 ) (y - intercept). The y - intercept is the point where ( x = 0 ), so the y - intercept should be at ( (0,6) ). But in the given graph, the line is horizontal (slope ( m = 0 )) and passes through ( y = 5 ), which is incorrect. To graph ( y=-\frac{1}{4}x + 6 ) correctly:

• Step 2: Plot the y - intercept Start by plotting the y - intercept. Since ( b = 6 ), we plot the point ( (0,6) ) on the y - axis.
• Step 3: Use the slope to find another point The slope ( m=-\frac{1}{4}=\frac{\text{rise}}{\text{run}} ). The rise is - 1 (down 1 unit) and the run is 4 (right 4 units). From the point ( (0,6) ), moving down 1 unit and right 4 units, we get the point ( (0 + 4,6-1)=(4,5) ). We can also use a positive rise over negative run: rise = 1 (up 1 unit) and run=-4 (left 4 units). From ( (0,6) ), moving up 1 unit and left 4 units, we get the point ( (0 - 4,6 + 1)=(-4,7) ).
• Step 4: Draw the line Draw a straight line through the points ( (0,6) ), ( (4,5) ), and ( (-4,7) ) to represent the equation ( y = -\frac{1}{4}x+6 ).

Answer:

The given graph is incorrect. To graph ( y = -\frac{1}{4}x + 6 ) correctly, plot the y - intercept at ( (0,6) ), then use the slope ( -\frac{1}{4} ) to find other points (e.g., ( (4,5) ) or ( (-4,7) )) and draw a line through them.