Question

Use a table of values to graph the equation. Label the \(x \text { -intercept and the } y \text { -intercept. (Review } 4.2,4.3)\) $$y=4 x-4$$

Short answer

The x-intercept of the equation y = 4x - 4 is x = 1 and the y -intercept is y = -4. Three points on the line are (-1,-8), (1,0) and (2,4).

Step-by-step solution

Identify the x and y-intercepts

The x-intercept is found by setting y = 0 and solving for x. This becomes 0 = 4x - 4, simplifying to x = 1. The y-intercept is found by setting x = 0 and solving for y. This becomes y = 4*0 - 4, simplifying to y = -4.

Generate a Table of Values

Choose at least two other arbitrary values for x and compute their corresponding y values using the linear equation y = 4x - 4. For a chosen x value of -1, y becomes 4*-1 - 4 = -8. For an x value of 2, y becomes 4*2 - 4 = 4.

Plot the Graph

Draw the axes and label them as 'x' and 'y'. Then, plot the generated table of values including the x and y intercepts on the graph. The three points are (-1,-8) corresponding to the arbitrary x=-1, (1,0) being the x-intercept, (0,-4) being the y-intercept, and (2,4) corresponding to the arbitrary x=2. Draw a straight line passing through all these plotted points.