Writing the Equation of a Line
Write linear equations in Grade 10 algebra using slope-intercept form y=mx+b, point-slope form, and standard form, given slope and a point or two coordinate pairs.
Key Concepts
New Concept If you know the slope $m$ and an ordered pair $(x 1, y 1)$ of any point on the line, you can use the point slope form to write the equation of the line. $$y y 1 = m(x x 1)$$.
Why it matters Algebra is the language used to describe relationships, and linear equations are its most fundamental sentences. Mastering how to write these equations from any given information is the key to unlocking mathematical modeling.
What’s next Next, you’ll apply these forms to solve problems, from converting temperatures to modeling real world business and growth data.
Common Questions
How do you write the equation of a line given slope m=3 and y-intercept b=−2?
Use slope-intercept form: y = mx+b = 3x-2. This is the simplest form when slope and y-intercept are known.
How do you write the equation of a line through (2,5) with slope 4?
Use point-slope form: y-5 = 4(x-2). Simplify to slope-intercept: y = 4x-3.
How do you write the equation of a line through (1,3) and (4,9)?
Find slope: m=(9-3)/(4-1)=2. Use point-slope with (1,3): y-3=2(x-1), giving y=2x+1.