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Identify the Slope and Intercept of a Line in Slope-Intercept Form
> ... Math > Slopes, Intercepts, Equation of a Straight Line > Identify the Slope and Intercept of a Line in Slope-Intercept Form

This is an introduction to drawing lines when given the slope and the y-intercept in an equation form. Remember that the y-intercept is where the graph crosses the y-axis; this is where we usually start. First, find the y-intercept, then determine the slope. For now, just focus on whether the slope is positive or negative.

Here are the variables we will start using in our function:

  • \( m = slope \)
  • \( b = y-intercept \)

The equation is y = mx + b. The x and y variables remain as letters, but m and b are replaced by numbers (ex: \( y = 2x + 4 \), \( slope = 2 \) and \( y-intercept = 4 \) ). The following video will show a few examples of understanding how to use the slope and intercept from an equation.

Identify the Slope and y-Intercept of an Equation Written in Slope-Intercept Form

Video Source (03:53 mins) | Transcript

\( y = mx + b \)

This equation is called the slope-intercept form because the two numbers in the equation are the slope and the intercept. Remember, the slope (m) is the number being multiplied to x and the intercept (b) is the number being added or subtracted.

Additional Resources

Practice Problems

1. Find the slope of the line:
\(\text{y}=6\text{x}+2\) (
Solution
x
Solution: 6
Details:
The equation of the line is written in the slope-intercept form, which is: \(y = {\color{Red}m}x + b\), where \({\color{Red}m}\) represents the \({\color{Red}slope}\) and b represents the y-intercept. In our equation, \(y = {\color{Red}6}x + 2\), we see that the slope of the line is \({\color{Red}6}\).
)2. Find the y-intercept of the line:
\({\text{y}}=-7{\text{x}}+4\) (
Solution
x
Solution: 4
Details:
The equation of the line is written in the slope-intercept form, which is: \(y = mx + {\color{Red}b}\), where m represents the slope and \({\color{Red}b}\) represents the \({\color{Red}y-intercept}\). In our equation, \(y=-7x+{\color{Red}4}\), we see that the \({\color{Red}y-intercept}\) of the line is \({\color{Red}4}\).
)3. Find the slope of the line:
\({\text{y}}=-3{\text{x}}+5\) (
Solution
x
Solution: \(-3\)
Details:
The equation of the line is written in the slope-intercept form, which is: \(y = {\color{Red}m}x + b\), where \({\color{Red}m}\) represents the \({\color{Red}slope}\) and b represents the y-intercept. In our equation, \(y={\color{Red}-3}x+5\), we see that the slope of the line is \({\color{Red}-3}\).
)4. Find the y-intercept of the line:
\({\text{y}}=-{\text{x}}-3\) (
Solution
x
Solution:
\(-3\)
)

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