Graphing linear functions using a single point and slope

Graphing linear functions using a single point and slope

If we are given a single point and the slope of a straight line, we will be able to graph it. By the same token, we can determine the slope and intercepts if we are given from its graph.
Basic Concepts: Solving linear equations by graphing, Slope intercept form: y = mx + b, Point-slope form: y−y1=m(x−x1)y - y_1 = m (x - x_1)
Related Concepts: Special case of linear equations: Horizontal lines, Special case of linear equations: Vertical lines, Parallel line equation, Perpendicular line equation

Lessons

  • 1.
    Graph the following line that passes through the given point and the slope
    a)
    (−3,2); (-3, 2) ; m =23 {2 \over 3}

    b)
    (4,−2); (4, -2); m = -35 {3 \over 5}

    c)
    (1,2); (1, 2); m = undefined

    d)
    (2,5); (2, 5); m = 0

    e)
    x int = 2; m = -1

    f)
    y int = -3; m = 32 {3 \over 2}

  • 2.
    Find the slope, x and y intercepts of each line.
    a)

    Graphing linear functions using a single point and slope

    b)

    Find x intercepts, y intercepts, and slope from the graph

    c)

    What is the x intercept, y intercept, and slope of the vertical line in the graph

    d)

    Determine the x intercept, y intercept and slope of the horizontal line from the graph

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12.
Linear Functions
12.1
Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
12.2
Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)
12.3
Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
12.4
Gradient intercept form: y = mx + b
12.5
General form: Ax + By + C = 0
12.6
Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1)
12.7
Rate of change
12.8
Graphing linear functions using table of values
12.9
Graphing linear functions using x- and y-intercepts
12.10
Graphing from gradient-intercept form y=mx+b
12.11
Graphing linear functions using a single point and gradient
12.12
Word problems of graphing linear functions
12.13
Parallel and perpendicular lines in linear functions
12.14
Applications of linear relations
NZ Year 10 Maths