Final answer:
The equation of the straight line which cuts off an intercept of 4 units from the y-axis and is equally inclined with the axes can be found using the slope-intercept form of a linear equation, y = mx + b. The equation of the straight line can be expressed as y = x + 4 or y = -x + 4.
Step-by-step explanation:
The equation of the straight line which cuts off an intercept of 4 units from the y-axis and is equally inclined with the axes can be found using the slope-intercept form of a linear equation, y = mx + b. In this case, the intercept on the y-axis is 4 units, so the y-intercept, b, is 4. Since the line is equally inclined with the axes, the slope, m, is the same for both the x and y axes.
If the slope is denoted as 'k', then the equation becomes y = kx + 4. To find the value of k, we can use the fact that the line is equally inclined with the axes. The slope of the line with respect to the x-axis is equal to the slope of the line with respect to the y-axis:
k = 1/k
Solving for 'k', we get k = 1 or k = -1. Therefore, the equation of the straight line can be expressed as y = x + 4 or y = -x + 4