graph this line using the slope and y - intercept:\n\n$y = - \\frac{1}{4}x + 1$\n\nclick to select points on…

graph this line using the slope and y - intercept:\n\n$y = - \\frac{1}{4}x + 1$\n\nclick to select points on the graph.

graph this line using the slope and y - intercept:\n\n$y = - \\frac{1}{4}x + 1$\n\nclick to select points on the graph.

Answer

Answer:

To graph the line ( y = -\frac{1}{4}x + 1 ), first plot the ( y )-intercept at ( (0,1) ). Then, use the slope ( -\frac{1}{4} ) (which means for every 4 units you move to the right along the ( x )-axis, you move 1 unit down along the ( y )-axis) to find another point. For example, from ( (0,1) ), moving 4 units right (to ( x = 4 )) and 1 unit down gives the point ( (4,0) ). Connect these two points with a straight line.

Explanation:

Step1: Identify the ( y )-intercept

The equation is in slope - intercept form ( y=mx + b ), where ( b = 1 ). So, the ( y )-intercept is at the point ( (0,1) ).

Step2: Use the slope to find another point

The slope ( m=-\frac{1}{4}=\frac{\Delta y}{\Delta x} ). Starting from ( (0,1) ), if ( \Delta x = 4 ) (move 4 units to the right), then ( \Delta y=- 1 ) (move 1 unit down). So, the new point is ( (0 + 4,1-1)=(4,0) ).

Step3: Draw the line

Connect the points ( (0,1) ) and ( (4,0) ) with a straight line. This line represents the equation ( y = -\frac{1}{4}x + 1 ).