The Slope-Intercept Form of a Linear Equation
Master slope-intercept form y=mx+b: identify slope m and y-intercept b directly from the equation, graph lines by plotting the intercept and using rise-over-run to find more points.
Key Concepts
A linear equation written in the form $y = mx + b$ is in slope intercept form. Here, $m$ represents the slope of the line, and $b$ represents the $y$ intercept.
For $y = \frac{1}{3}x + 2$, the slope is $ \frac{1}{3}$ and the y intercept is $2$. Start at $(0, 2)$, then move down 1 unit and right 3 units to find the next point at $(3, 1)$. To graph $4x + 2y = 8$, first solve for $y$: $2y = 4x + 8$, which gives $y = 2x + 4$. The slope is $ 2$ and the y intercept is $4$. Start at $(0, 4)$ and move down 2, right 1.
This form is a graphing treasure map! The equation literally hands you your starting point, $b$ (where the line crosses the y axis), and your directions, $m$ (the slope), to find the next point on the map. No tables, no extra math, just pure graphing action!
Common Questions
What information does slope-intercept form reveal immediately?
Slope-intercept form y=mx+b reveals the slope m (rise over run) and the y-intercept b (where the line crosses the y-axis) directly from the equation without any calculation. For y=3x-4, slope is 3 and y-intercept is -4, so the line crosses at (0,-4) and rises 3 units for every 1 unit right.
How do you graph a line from slope-intercept form?
Plot the y-intercept at (0,b) on the y-axis. From that point, use the slope m=rise/run to find a second point: move up by the numerator and right by the denominator (or down and left for negative slopes). Draw a straight line through the two points and extend with arrows.
How do you convert standard form to slope-intercept form?
Solve Ax+By=C for y. Subtract Ax from both sides: By=C-Ax. Divide by B: y=(-A/B)x+(C/B). The slope is -A/B and the y-intercept is C/B. For 2x+3y=12: 3y=-2x+12, then y=(-2/3)x+4.