Question

Graph the equation. $$y=x+4$$

Short answer

The graph of the equation \(y = x + 4\) is a straight line with slope 1, intersecting the y-axis at the point (0,4).

Step-by-step solution

Identify the slope and the y-intercept

The equation, \(y = x + 4\) is in slope-intercept form, \(y = mx + c\). Here, \(m = 1\) and \(c = 4\). So, the slope of the line is 1 and the line intersects the y-axis at the point (0, 4).

Plot the y-intercept

First, plot the y-intercept on graph which is at point (0,4). This will be the initial point on the line.

Use the slope to find the next point

The slope of the line is the ratio of the change in y to the change in x. Since the slope is 1, for every 1 unit increase in x, y should also increase by 1 unit. Now from the y-intercept (0, 4), move 1 unit right and 1 unit up to plot the next point (1, 5).

Draw the line

Now, connect the points (0,4) and (1,5) and extend the line in both directions. This line represents the graph of the equation \(y = x + 4\).