Slope-Intercept Form

Learn and use y = mx + b form of linear equations. Math 10-C Alberta mathematics curriculum.

Lesson 6.3 of Linear Relations and Functions in Math 10C: Alberta curriculum lessons.

What you'll learn in this lesson

• Understanding y = mx + b. Learn the meaning of slope and y-intercept in the slope-intercept form. Discover how to read m and b from a real-world graph and find the equation of a line using two points.
• Writing Equations and Converting Forms. Practice writing the equation of a line from a graph and converting standard-form equations into slope-intercept form by solving for y.
• Real-World Applications. Apply slope-intercept form to real-world scenarios. Interpret slope and y-intercept in context, find break-even points, and determine when answers must be whole numbers.

Inside the lesson: a free preview

The Slope-Intercept Equation

What Each Part Means. m is the slope, it measures the rate of change, describing how steep the line is and in which direction it goes.

b is the y-intercept. It is the value of y when x = 0, which is exactly where the line crosses the y-axis.

This form immediately tells you two things about a line: its steepness and direction (m), and where it starts on the y-axis (b).

Reading m and b from a Real-World Graph

The Cyclist's Journey. A graph shows a cyclist's distance from home (km) over time (hours). The line starts at 10 km when time = 0 and rises steadily.

y-intercept (b = 10): At time 0, the cyclist is already 10 km from home. This is the starting position.

Slope (m): The slope equals (rise)/(run) = (km)/(h). The slope tells you the cyclist's speed. The units come from the axes, distance (km) divided by time (h) gives km/h.

Key Insight: Interpreting m and b. The y-intercept is the starting value, what is happening when x = 0.

The slope is the rate of change, how fast the dependent variable changes per unit of the independent variable.

Worked example: Cell Phone Plan

Example 1: Cell Phone Plan. A cell phone plan includes the first 300 minutes free. A graph shows the cost based on minutes used beyond 300. Two points on the graph are (0, 20) and (50, 35).

Step 1: Find the slope:

m = (35 - 20)/(50 - 0) = (15)/(50) = (3)/(10)

This means the plan charges \0.30 per extra minute beyond 300.

Step 2: Read the y-intercept:

b = 20

The base cost of the plan is \20 (covering the first 300 minutes).

Step 3: Write the equation:

y = (3)/(10)x + 20

where y is the total cost in dollars and x is the number of minutes beyond 300.

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