Linear Equations: Graphing in Standard Form vs Slope-Intercept Form
Learn how to convert linear equations from standard form to slope-intercept form for easier graphing and interpretation. Discover how to find intercepts and analyze slopes and y-intercepts to graph lines effectively in mathematics.
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Presentation Transcript
STANDARD FORM Standard form of a linear equation is written in the form of Ax + By + C = 0 Graphing from standard form is trickier than graphing from slope, y-intercept form SO You can change a standard form equation into slope y-intercept form by rearranging the equation to look like ___________________. ? = ?? + ? But one thing it's very good at is finding the x- and y-intercepts of a line. The x-intercept occurs when y=0. Similarly, the y-intercept occurs when x=0. So to find these, you just need to plug in x=0 and solve for y, then plug in y=0 and solve for x.
2. 3? ? 6 = 0 ? = 3? + 6 ? = 3? 6 ? = 3 ? = 6 ? = 3? 6
Using the Standard Form to Determine Intercepts 3? ? 6 = 0 To find out where this graph crosses the y axis, set x to 0 3 0 ? 6 = 0 ? = 6 The graph crosses the y-axis at the point 0,-6 ? = 6 To find out where this graph crosses the x axis, set y to 0 3? 0 6 = 0 3? = 6 ? = 6 The graph crosses the x-axis at the point -2, 0 3 Setting x to zero gives you the y-intercept. Setting y to zero gives you the x-intercept.
Example: Change x + 3 to slope y-intercept form. = y 2 6 0 3? + 2? 6 = 0 2? = 3? + 6 2 3 2 6 2 y x+ = 2 3 2 = + 3 y x What is the slope & y-intercept? ? = 3 y intercept is 3 2
Rearrange the following equations from standard form to slope, y-intercept form. ? + ? 3 = 0 ? ? = 0 2? + 5? 15 = 0 ? = ? + 3 5? = 2? + 15 ? = ? 5? 5=2? 5+15 ? = ? 5 ? =2 5? + 3 ? = 1 ? = 0 ? = 1 ? = 3 ? =2 ? = 3 5
CHANGE FROM STANDARD FORM TO SLOPE Y-INTERCEPT FORM, THEN GRAPH a)Rewrite the standard form equation in Slope y-intercept form ( y b)State the slope and y-intercept c)Graph and label the line = + ) and mx b 1. 2? + ? + 4 = 0 ? = 2? 4 ? = 2 ? = 4 ? = 2? 4
3. 3? + 2? 4 = 0 2? = 3? + 4 2? 2= 3? +4 2 2 ? = 3 2? + 2 ? = 3 2? + 2 ? =3 ? = 2 2
