Write the equation of a line and fit lines to data
Write, compare, transform, and model linear equations, and fit lines to data.
Common CoreA-CED.A.2S-ID.B.6S-ID.C.7
6 lessons21 short videos5 key concepts, out loud
6.1
Point-Slope Form
Write a line from a point and a slope
A-CED.A.2
Key idea
Write the equation of a line using point-slope form, y - y1 = m(x - x1), by substituting a given slope for m and the coordinates of a given point for (x1, y1).
Learn how to write the equation of any line instantly using just its slope and a single point on its path.
Key concept · Lesson 6.1
Subtract the point, always
Listen0:00 / 0:21
Transcript. Point-slope form is built for exactly what you are given: one point and one slope. Substitute the slope for m and the coordinates for x one and y one, keeping the subtraction signs. When a coordinate is negative, subtracting it turns into adding, so watch both signs.
6.2
Writing Equations from Two Points
Find the slope, then build the equation
A-CED.A.2
Key idea
To write the equation of a line from two points, first calculate the slope, then substitute the slope and either given point into point-slope or slope-intercept form to solve for the final equation.
Learn how to find the slope between two points and use it to write the complete linear equation.
Key concept · Lesson 6.2
Slope first, then one point
Listen0:00 / 0:22
Transcript. Two points are enough to write any line. First use them to find the slope, subtracting in a consistent order. Then substitute that slope and either one of the points into point-slope form. Both points give the same final answer, so never mix coordinates from different pairs.
6.3
Standard Form & Converting Between Forms
Ax + By = C, and how to switch forms
A-CED.A.2
Key idea
Standard form (Ax + By = C) groups both variable terms on one side and the constant on the other, and you can convert between any linear forms by using inverse operations to isolate variables or clear fractions.
Learn how to write linear equations in standard form and master the algebraic steps to switch between any of the three main forms of a line.
Key concept · Lesson 6.3
One line, three forms
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Transcript. Standard form puts both variable terms on one side and the constant on the other. Slope-intercept and point-slope arrange the same line differently. Convert with ordinary inverse operations: clear fractions, then move terms across, remembering that a term changes sign as it crosses.
6.4
Parallel & Perpendicular Lines
Lines that never meet or meet at a right angle
A-CED.A.2
Key idea
Parallel lines have identical slopes, while perpendicular lines have slopes that are negative reciprocals of each other, allowing you to write the equation of a new line based on its relationship to an existing one.
Learn how to identify parallel and perpendicular lines by comparing their slopes, and write equations for lines that run parallel or perpendicular to a given line through a specific point.
Key concept · Lesson 6.4
Build from Equation A
Listen0:00 / 0:21
Transcript. Parallel lines never meet because their slopes are identical, so copy the slope straight across. Perpendicular lines meet at a right angle, and their slopes are negative reciprocals: flip the fraction and change the sign. Either way, use the new point, not the old intercept.
6.5
Scatter Plots & Line of Best Fit
Model real data with a trend line
S-ID.B.6S-ID.C.7
Key idea
To model bivariate data, draw a line of best fit through the center of a scatter plot and write its linear equation to make predictions and interpret the real-world meaning of its slope and y-intercept.
Learn how to draw a trend line through a scatter plot, write its linear equation, and use it to make predictions about real-world data.
Key concept · Lesson 6.5
Balance the dots, then predict
Listen0:00 / 0:21
Transcript. A line of best fit summarises a cloud of points. Draw one straight line through the middle, with roughly half the points above and half below. Do not connect the dots or force it through the origin. Its slope is the rate, and its intercept is the starting value.
6.6
Review & Assessment
Writing and modeling with lines
Review, practice, quiz and test
Key idea
Review equation writing with targeted practice, a practice test, and a chapter test.
This is one chapter of the climb.
Algebra 1 spans 16 chapters, every lesson taught on video with a key concept you can hear, and Vector on hand to answer questions out loud.
