Unit 4: Forms of Linear Equations
The same line written three different ways -- slope-intercept, point-slope, and standard form -- plus what makes two lines parallel or perpendicular.
7 topics · 26 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
Slope-Intercept Form
- How it worksHow does reading off m and b from y = mx + b place a line on the graph without plotting points?
- Worked exampleGraph the line y = -3x + 2 using its slope and y-intercept.
- Common mistakeWhy isn't the b in y = mx + b the line's slope?
- Going furtherWhat happens to a line's graph when only its y-intercept changes and its slope stays fixed?
Your turn1 of 2
For the line y = -3x + 6, find the value of y when x = 6.Point-Slope Form
- How it worksHow does point-slope form build a line's equation directly from a slope and a single known point?
- Worked exampleFind the point-slope equation of the line through (2, -1) with a slope of 3.
- Worked exampleFind the slope-intercept form of the point-slope equation y - 4 = 2 times the quantity x minus 1.
- Common mistakeWhy doesn't the point plugged into point-slope form have to be the y-intercept?
Your turn1 of 2
A line passes through (6, 8) with slope 7. Write its equation in slope-intercept form (y in terms of x).Standard Form of a Linear Equation
- How it worksHow do you find both intercepts of a line straight from its standard form without graphing?
- Worked exampleFind the intercepts of the line 4x - 5y = 20 written in standard form.
- Common mistakeWhy doesn't the A in standard form Ax + By = C tell you the line's slope directly?
- Worked exampleFind the slope of the line 6x - 3y = 12 by first solving for y.
Your turn1 of 2
Find the x-intercept of the line 7x - 7y = 57.Converting Between Forms
- How it worksHow does solving for y turn any linear equation into slope-intercept form?
- Worked exampleFind the slope-intercept form of 3x + 2y = 8.
- Worked exampleFind the standard form of y = -4x + 7.
- Going furtherWhat happens to a line's graph when you convert its equation to a different form?
Your turn1 of 2
Convert 7x + 7y = 57 to slope-intercept form. Write y in terms of x.Writing an Equation Through Two Points
- How it worksHow does finding the slope between two points let you then write the line's full equation?
- Worked exampleFind the equation of the line through (2, 5) and (6, 13).
- Common mistakeWhy doesn't it matter which of the two points you plug into point-slope form first?
Your turn1 of 2
Find the equation of the line through (3, 6) and (9, 16), in slope-intercept form (y in terms of x).Parallel Lines
- How it worksHow does comparing two equations' slopes tell you instantly whether their lines are parallel?
- Worked exampleFind the equation of the line through (1, 4) that is parallel to y = 2x - 3.
- Common mistakeWhy doesn't having the same y-intercept make two lines parallel?
Your turn1 of 2
Find the equation, in slope-intercept form, of the line through (8, 3) that is parallel to y = 7x + 6.Perpendicular Lines
- How it worksHow does multiplying two slopes together to get -1 confirm that two lines are perpendicular?
- Worked exampleFind the equation of the line through (3, -2) that is perpendicular to a line with slope 2.
- Common mistakeWhy doesn't a perpendicular slope just mean the negative of the original slope?
- Going furtherWhat happens to the perpendicular-slope rule when the original line is perfectly horizontal?
Your turn1 of 2
Find the equation, in slope-intercept form, of the line through (6, 8) that is perpendicular to a line with slope 5.