Slope-Intercept Form: y = mx + b
Grade 9 students in California Reveal Math Algebra 1 learn the slope-intercept form y=mx+b, the most useful way to write a linear equation because it immediately reveals two key features. The coefficient m is the slope — how steep the line is and in which direction it tilts. The constant b is the y-intercept — exactly where the line crosses the y-axis. For example, y=3x+2 has slope 3 and y-intercept 2; y=-1/2x+5 has slope -1/2 and y-intercept 5; and y=4x-7 crosses the y-axis at (0,-7). Students use this form to write linear equations by identifying slope and intercept first.
Key Concepts
The slope intercept form of a linear equation is:.
Common Questions
What is slope-intercept form?
Slope-intercept form is y=mx+b, where m is the slope of the line and b is the y-intercept — the point where the line crosses the y-axis.
How do you identify the slope and y-intercept from y=3x+2?
In y=3x+2, the coefficient of x is m=3 (the slope) and the constant is b=2 (the y-intercept). The line rises 3 units for every 1 unit to the right and crosses the y-axis at (0,2).
What does a negative slope mean in slope-intercept form?
A negative slope means the line tilts downward from left to right. For y=-1/2x+5, the line falls 1/2 unit for every 1 unit to the right.
How do you write a linear equation in slope-intercept form?
Identify the slope m (the rate of change) and the y-intercept b (the starting value), then substitute directly into y=mx+b.
What does the y-intercept tell you about the graph?
The y-intercept b tells you exactly where the line crosses the y-axis. For y=4x-7, b=-7 means the line crosses at the point (0,-7).
Which unit covers slope-intercept form in Algebra 1?
This skill is from Unit 4: Creating Linear Equations in California Reveal Math Algebra 1, Grade 9.