Write the equation of a line from its slope and y-intercept

A line with slope $m$ and $y$ -intercept $b$ is represented by $y=mx+b$ , where $m$ describes the constant rate of change and $b$ is the value of $y$ when $x=0$ , so its graph passes through $(0,b)$ . This understanding includes positive, negative, zero, and fractional slopes and supports translating between an equation, a graph, and a verbal relationship; vertical lines, undefined slopes, and more advanced forms of line equations are not included.

Detailed Explanation: Write the equation of a line from its slope and y-intercept

A line with slope $m$ and $y$ -intercept $b$ can be written in slope-intercept form:

y=mx+b

To write the equation:

Identify the slope $m$ .
Identify the $y$ -intercept $b$ .
Substitute those values into $(y=mx+b)$ .
Simplify if needed.

Example: Write the equation of a line with slope $(-\frac{2}{3})$ and $y$ -intercept $4$ .

The slope is

m=-\frac{2}{3}

and the $y$ -intercept is

b=4.

Substitute these values into the formula:

y=mx+b

y=-\frac{2}{3}x+4

So, the equation of the line is

\boxed{y=-\frac{2}{3}x+4}

The $y$ -intercept of $4$ means the line passes through $((0,4))$ . The slope $(-\frac{2}{3})$ means that for every $3$ units moved to the right, the line moves $2$ units down.

Learn by doing: Write the equation of a line from its slope and y-intercept

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Practice with unlimited practice problems

Slope of a Line - Select Linear Equation Based on Graph

Earned ?

Write the equation of a line from its slope and y-intercept

Detailed Explanation: Write the equation of a line from its slope and y-intercept

Learn by doing: Write the equation of a line from its slope and y-intercept

Practice with unlimited practice problems

Practice:

Slope of a Line - Select Linear Equation Based on Graph