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Understanding Graphing Lines: Linear Equations and Their Forms

This guide explores the key concepts of graphing lines in mathematics, focusing on the different forms of linear equations: point-slope form, standard form, and slope-intercept form. It details how to derive equations based on gradients and specific points, as well as how to graph lines using x and y-intercepts. Additionally, it covers methods for finding the intersection of lines. Exercises are provided for practice, enhancing your understanding of these mathematical concepts.

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Understanding Graphing Lines: Linear Equations and Their Forms

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  1. Material Taken From:Mathematicsfor the international student Mathematical Studies SLMal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark BruceHaese and Haese Publications, 2004

  2. 7G Graphing Lines Forms of a Linear Equation point-slope form standard form slope-intercept form y – y1 = m(x – x1) y = mx + b Ax + By = C slope point

  3. Find, in standard form, the equation of the line with gradient -5/6 and passing through (8, -7).

  4. Section 7g - Graphing Lines Slope-intercept form x- and y-intercepts

  5. Graphing Lines Slope-intercept form x- and y-intercepts y = mx + b 1) solve the equation for y. 2) plot the y-intercept 3) use the slope to find another point 4) draw the line

  6. Graph using the slope and y-intercept.

  7. Lines x-intercept y-intercept

  8. Graphing Lines Slope-intercept form x- and y-intercepts y = mx + b 1) find the x-intercept by letting y = 0 1) solve the equation for y. 2) find the y-intercept by letting x = 0 2) plot the y-intercept 3) use the slope to find another point 3) plot the intercepts. 4) draw the line 4) draw the line

  9. Graph by finding the x- and y-intercepts. 2x – 3y = 12

  10. Graph by finding the x- and y-intercepts. x + 2y = 4

  11. See page 227 Where Graphs Meet…

  12. Graph the lines, find where they meet x + y= 6 2x – y = 6

  13. Use Autograph to find where the lines meet 4x + 3y = 10 x – 2y = -3

  14. Use your calculator to find where the lines meet y = x + 4 5x – 3y = 0

  15. Homework • You will need graph paper to do this: • Exercise 7G.1, pg226 • #1adg, 2ag • Exercise 7G.2, pg229 • #1a, 3ad

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