Converting Point-Slope to Slope-Intercept Form
Converting point-slope form to slope-intercept form is a core Algebra 1 skill in enVision Chapter 2 for Grade 11. Starting from y - y₁ = m(x - x₁), distribute the slope, then isolate y by moving the constant to the right side to reach y = mx + b format. For example, y - 3 = 2(x - 1) becomes y = 2x + 1 after distributing and adding 3. This conversion is useful because slope-intercept form directly reveals both the slope and y-intercept, making graphing and comparison straightforward. Students practice multiple conversions including those with fractional slopes such as y + 4 = -½(x - 6).
Key Concepts
To convert from point slope form to slope intercept form, solve for $y$: $$y y 1 = m(x x 1) \rightarrow y = mx mx 1 + y 1$$.
Common Questions
What is the first step to convert point-slope to slope-intercept form?
Distribute the slope to both terms inside the parentheses. For y - 3 = 2(x - 1), distribute to get y - 3 = 2x - 2.
After distributing, how do you finish the conversion?
Add or subtract the constant on the left side to both sides to isolate y. For y - 3 = 2x - 2, add 3 to get y = 2x + 1.
How do you handle fractional slopes when converting?
Distribute the fraction to each term in parentheses. For y + 4 = -½(x - 6), distribute to get y + 4 = -½x + 3, then subtract 4: y = -½x - 1.
Why is slope-intercept form useful after converting?
Slope-intercept form y = mx + b directly shows the slope m and y-intercept b, making it easy to graph the line or compare it to other lines.
What does the converted form y = -3x - 6 tell you about the line?
The slope is -3 (falls 3 units for every 1 unit right) and the y-intercept is -6, meaning the line crosses the y-axis at (0, -6).