Sketch the graph of g(x) = - 4x + 8?

Answer 1

To sketch the graph of ( g(x) = -4x + 8 ), we can follow these steps:

1. Determine the y-intercept: The y-intercept is the point where the graph intersects the y-axis. For the equation ( g(x) = -4x + 8 ), the y-intercept occurs when ( x = 0 ). Substitute ( x = 0 ) into the equation to find the y-intercept:

[ g(0) = -4(0) + 8 = 8 ]

So, the y-intercept is ( (0, 8) ).

2. Determine the slope: The coefficient of ( x ) in the equation represents the slope of the line. For ( g(x) = -4x + 8 ), the slope is ( -4 ).

3. Use the slope and the y-intercept to plot a second point: Since the slope is ( -4 ), it means that for every unit increase in ( x ), ( y ) decreases by 4 units. Starting from the y-intercept ( (0, 8) ), we can move down 4 units (due to the negative slope) and one unit to the right to find another point. This gives us the point ( (1, 4) ).

4. Plot the points and draw the line: Plot the points ( (0, 8) ) and ( (1, 4) ) on the coordinate plane, then draw a straight line passing through these points. This line represents the graph of ( g(x) = -4x + 8 ).

Here's the sketch of the graph: