📚 Practice With Worksheets
Practice identifying slope and intercepts, interpreting linear equations, and writing equations from points.
▶️ Learn With Videos
Review how slope-intercept form, graphed lines, and the slope formula connect equations, points, and graphs.
🛠️ How to Use This Tool
Choose Slope-Intercept Line to explore equations in the form \(y=mx+b\). Move the slope and y-intercept sliders and watch the graph respond immediately.
Use the Focus Question, What to Notice, and Current Observation sections to connect each slider value to the direction, steepness, and position of the line. The formatted equation updates after the slider is released.
Choose Vertical Line to explore equations in the form \(x=c\). Use Show Reference Line \(y=x\) when a comparison is helpful, and zoom, pan, or center the graph as needed.
🧠 Things to Notice
Positive slopes rise from left to right, negative slopes fall, and a slope of zero creates a horizontal line. Larger values of \(|m|\) make a line steeper, while values closer to zero make it shallower.
Changing \(b\) moves a line up or down without changing its slope. Lines with the same slope but different y-intercepts are parallel.
Horizontal lines have slope zero and equations such as \(y=k\). Vertical lines have undefined slope and equations such as \(x=c\), so they cannot be written in slope-intercept form.
📘 Vocabulary
Linear Equation: An equation whose graph is a straight line.
Slope: A measure of a line’s direction and steepness, calculated as the change in \(y\) divided by the change in \(x\).
Rate of Change: The amount the output changes for each one-unit change in the input.
Slope-Intercept Form: The form \(y=mx+b\), where \(m\) is the slope and \(b\) is the y-intercept.
y-Intercept: The point where a graph crosses the y-axis. At this point, \(x=0\).
x-Intercept: The point where a graph crosses the x-axis. At this point, \(y=0\).
Positive Slope: A slope that makes a line rise from left to right.
Negative Slope: A slope that makes a line fall from left to right.
Zero Slope: The slope of a horizontal line. Its output remains constant.
Undefined Slope: The slope of a vertical line, where the horizontal change is zero.
Horizontal Line: A line with an equation such as \(y=k\) and a slope of zero.
Vertical Line: A line with an equation such as \(x=c\) and an undefined slope.
Parallel Lines: Lines in the same plane that have equal slopes and never intersect.
Reference Line: A comparison graph, such as \(y=x\), used to notice changes in slope, direction, or position.
📐 Concepts for Reading Linear Graphs
In slope-intercept form, \(m\) controls the direction and steepness of the line, while \(b\) identifies where the line crosses the y-axis.
\(y=mx+b \qquad m=\dfrac{\text{rise}}{\text{run}}\)
The reference line \(y=x\) has slope \(1\) and y-intercept \(0\). A line with \(|m|>1\) is steeper than \(y=x\), while a nonzero slope with \(|m|<1\) is shallower.
\(y=x \qquad m=1,\ b=0\)
To find the y-intercept, set \(x=0\). To find the x-intercept, set \(y=0\). These intercepts show where a line crosses the coordinate axes.
\(\text{y-intercept: }x=0 \qquad \text{x-intercept: }y=0\)
Horizontal lines have equations of the form \(y=k\) and slope \(0\). Vertical lines have equations of the form \(x=c\) and undefined slope because their horizontal change is zero.
\(y=k \Rightarrow m=0 \qquad x=c \Rightarrow m\text{ is undefined}\)
🔗 Share This Math Tool
Found this resource helpful? Share it with another teacher or save the link for later.
🚀 Explore More Math Tools
Browse more interactive tools for algebra, graphing, functions, equations, geometry, ratios, probability, statistics, and number systems.
Explore More Math Tools