What information can be extracted from the equation y = 4x + 5?
Understand the Problem
The question is asking us to define the equation of a straight line. The equation is already given in slope-intercept form, where we can identify the slope and y-intercept directly.
Answer
$m$ = slope $b$ = y-intercept
Answer for screen readers
The equation of a straight line in slope-intercept form is $y = mx + b$, where:
$m$ = slope
$b$ = y-intercept
Steps to Solve
- Recall the slope-intercept form
The slope-intercept form of a line is given by the equation $y = mx + b$, where $m$ represents the slope of the line and $b$ represents the y-intercept.
- Identify the slope
In the equation $y = mx + b$, the coefficient of $x$ gives us the slope of the line. So the slope is $m$.
- Identify the y-intercept
In the equation $y = mx + b$, the constant term gives us the y-intercept. So the y-intercept is $b$.
The equation of a straight line in slope-intercept form is $y = mx + b$, where:
$m$ = slope
$b$ = y-intercept
More Information
The slope-intercept form is a particularly useful way to represent linear equations because it allows you to immediately identify two key properties of the line: its slope and where it intersects the y-axis. This form makes it easy to graph the line and understand its behavior.
Tips
A common mistake is confusing the slope and y-intercept. The slope is always the coefficient of $x$, and the y-intercept is the constant term. Another mistake involves incorrectly plotting the y-intercept or using the slope in the wrong direction when graphing the line.
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