graph the line with the equation $y = \\frac{1}{4}x + 1$.

graph the line with the equation $y = \\frac{1}{4}x + 1$.

graph the line with the equation $y = \\frac{1}{4}x + 1$.

Answer

Explanation:

Step1: Identify y-intercept

The equation ( y = \frac{1}{4}x + 1 ) is in slope - intercept form (( y = mx + b )), where ( b = 1 ). So the line crosses the y - axis at ( (0, 1) ).

Step2: Determine slope and find another point

The slope ( m=\frac{1}{4} ) (rise = 1, run = 4). From ( (0, 1) ), move up 1 unit and right 4 units: ( (0 + 4, 1+1)=(4, 2) ). Alternatively, for ( x=-4 ), ( y=\frac{1}{4}(-4)+1 = 0 ), so ( (-4, 0) ) is also on the line.

Step3: Plot points and draw the line

Plot ( (0, 1) ) (y - intercept) and ( (4, 2) ) (or ( (-4, 0) )). Draw a straight line through these points to represent ( y=\frac{1}{4}x + 1 ).

Answer:

To graph ( y=\frac{1}{4}x + 1 ):

  1. Plot the y - intercept ( (0, 1) ).
  2. Use the slope ( \frac{1}{4} ) to plot a second point (e.g., ( (4, 2) ) or ( (-4, 0) )).
  3. Draw a straight line through the plotted points.

(Note: The graph should be a straight line passing through ( (0, 1) ), ( (4, 2) ), and ( (-4, 0) ), etc.)