Draw and read graphs on the coordinate plane, from single points and straight lines to powers and parabolas. Find where two graphs meet, shade the regions that inequalities describe, and graph curves written with as the subject.
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The equation of a straight line
Learn how to read the slope and -intercept of a straight line from its equation in slope-intercept form, find the equation of a line drawn on a grid, and write the equations of horizontal and vertical lines.
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Curves given as in terms of
Learn how to graph equations that have as the subject, from straight lines to parabolas turned on their side, and how to rewrite a line or a parabola with the other variable as the subject, choosing the right sign for each branch.
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Lesson 04 · The equation of a straight line
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The 12 lessons in this unit. Expand any one to see what it covers. Each unlocks when its own prerequisites are passed.
01
The coordinate plane
8 questions
Learn how to read the coordinates of a point marked on the coordinate plane, and how to plot a point from its coordinates.
Covers
Reading a point's coordinates
Plotting a point from its coordinates
02
The graph of an equation
13 questions
Learn how to decide whether a point lies on the graph of an equation, graph an equation by plotting a table of values, and read values off a graph.
Covers
Deciding whether a point is on a graph
Graphing an equation by plotting points
Reading values off a graph
03
The slope of a line
12 questions
Learn how to find the slope of a straight line from two of its points, read the sign and steepness of a slope from a picture, and see why horizontal lines have slope and vertical lines have undefined slope.
Covers
Slope from two points
Reading slope from a picture
Slopes of horizontal and vertical lines
04
The equation of a straight line
12 questions
Learn how to read the slope and -intercept of a straight line from its equation in slope-intercept form, find the equation of a line drawn on a grid, and write the equations of horizontal and vertical lines.
Covers
The slope-intercept form
Finding the equation of a drawn line
The horizontal or vertical line through a point
05
Point-slope form of a line
14 questions
Learn how to write the equation of the straight line through a point with a given slope in point-slope form, find the line through two points, and rewrite it in slope-intercept form.
Covers
The line through a point with a given slope
The line through two points
Converting to slope-intercept form
06
Graphs of power functions
12 questions
Learn the shapes of the square, cube and square-root curves, the symmetry behind each shape, and which curve is highest on either side of .
Covers
The symmetries of and
The curve of
Comparing heights of the curves
07
Parabolas and their turning points
8 questions
Learn how to tell which way a parabola opens and where it crosses the -axis from its equation, and how to locate its turning point midway between the points where it crosses the -axis.
Covers
The parabola and which way it opens
Locating the turning point
08
Where two graphs meet
14 questions
Learn how to find where a parabola meets a line or another parabola by setting their equations equal and solving, and how to use the discriminant to count the points of intersection without solving.
Covers
The equation for the points of intersection
Finding the points of intersection
Counting points of intersection with the discriminant
09
Two-variable inequalities
12 questions
Learn how to shade the region where an inequality in two variables holds, on the correct side of its boundary line or curve, and how solid and dashed boundaries tell non-strict and strict inequalities apart.
Covers
Horizontal and vertical boundaries
Shading the region of an inequality
Solid and dashed boundaries
10
Regions where two conditions hold
10 questions
Learn how to pick out the region where two conditions in and both hold, find the smallest rectangle that contains a bounded region, and recognise when a region is unbounded.
Covers
The overlap of two regions
Bounded and unbounded regions
11
Describing planar regions
8 questions
Learn how to write a region of the plane as a set of points in set-builder notation, from half-planes and rectangles to regions bounded by curves, and how an equation gives a curve while an inequality gives a region.
Covers
A region as a set
Curves and regions as sets
12
Curves given as in terms of
13 questions
Learn how to graph equations that have as the subject, from straight lines to parabolas turned on their side, and how to rewrite a line or a parabola with the other variable as the subject, choosing the right sign for each branch.
Covers
Lines with as the subject
Sideways parabolas
The same curve written both ways
This unit is part of our Mathematical Foundations for ML learning path, which contains 95 lessons. Every one of them is drawn below.
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12 lessons in this unit
13 prerequisite lessons across the unit, counting every step back to the start
70 other lessons in the learning path - after this unit, or alongside it
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More in Mathematical foundations: Inequalities and absolute value, Quadratic equations, Set operations, Exponents and roots, Functions, Summation, product, and indexed notation, Logic, Exponentials and logarithms, Trigonometry