The graph of an equation in the form y=mx + b is a
straight line. Can the equation of every straight line be
written in the form y=mx + b (Hint: What is the
equation of a vertical line?)
No, the equation of every straight line cannot be written in the form y=mx + b. The equation y=mx + b represents a linear equation in slope-intercept form, where m is the slope of the line and b is the y-intercept. This form can be used to represent any straight line except for vertical lines.
The equation of a vertical line is of the form x = c, where c is a constant. In this case, there is no y-intercept, and the slope is undefined (or infinite). Therefore, the equation of a vertical line cannot be written in the form y=mx + b.
For example, the equation x = 3 represents a vertical line that crosses the x-axis at x=3. This equation cannot be written in the form y=mx + b.
The equation of a straight line in the form y = mx + b is called the slope-intercept form, where m represents the slope of the line and b represents the y-intercept.
But can every straight line be written in this form?
The answer is mostly yes, but there is an exception for vertical lines. A vertical line has an undefined slope since the change in x is always zero.
The equation of a vertical line is of the form x = c, where c is a constant. This equation gives us the x-coordinate of every point on the line and does not have a y-intercept.
Therefore, while the equation y = mx + b can represent the equation of any straight line, it cannot represent vertical lines. For vertical lines, we need to use the equation x = c.