Flashback! 13.6 & 13.7 (Part 1) Graphing Equations of Lines & Writing Equations of Lines Geometry Honors- Watanabe Point-Slope, Slope Intercept & Standard Form

Where m is the slope and b is the intercept What we know so far…. Slope Intercept Form Where m is the slope and b is the intercept

Where two points are given as (x1,y1) and (x2,y2) What we know so far…. Slope Where two points are given as (x1,y1) and (x2,y2)

Recall… Write equations Slope-intercept form is: Where m is the slope and b is the y-intercept Example: Find the equation of the line with slope -2 and y-intercept 8 y = -2x + 8 Easy if I know the y-intercept… but if I don’t?

Might be new to some… Point- Slope form is: Where m is the slope and (x1,y1) is the given point that the line goes through

Where does this equation come from? Point- Slope Form Point- Slope form is: Where does this equation come from?

Using Point-Slope Form to graph 1 2 4 3 5 -1 -2 -3 -4 -5 Slope is Point is (2,3)

Manipulate Point-Slope Form to Slope-Intercept form Simplify

Using Point-Slope Form to graph 1 2 4 3 5 -1 -2 -3 -4 -5 Slope is Point is (4,-3)

Manipulate Point-Slope Form to Slope-Intercept form

Your turn

Forms of a linear equation (You need to know these!) Slope-intercept Form y = mx + b Standard Form Ax + By = C Point-Slope Form y – y1 = m(x – x1)

If given the slope and y-intercept, use slope-intercept form. Example m = 5, b = 7 5 7 y = ___ x + ___

If given the a point and the slope, There are two methods that are both effective. The time required and the number of steps for the two methods is comparable. Know how to do both, but typically Either will work just fine.

If given the a point and the slope, Step 1 Method 1 use slope-intercept form. Substitute –2 for m, 5 for x & –8 for y; then simplify to find the value of b. y = mx + b –8 = –2(5) + b –8 = –10 + b 2 = b Example m = –2, contains (5, –8) Step 2 Substitute –2 for m, and 2 for b. y = –2x + 2

If given the a point and the slope, Method 2 use point-slope form. (My preferred method to start with) Substitute –2 for m, 5 for x1, and –8 for y1; then simplify and solve the equation for y . y – y1 = m(x – x1) y – (– 8) = – 2(x – 5) y + 8 = –2x + 10 Example m = –2, contains (5, –8) y = –2x + 2

If given two points, Then use the slope and EITHER point to work like the previous example. y – y1 = m(x – x1) y – 7 = – 5(x – 2) y – 7 = –5x + 10 m = –5, contains (5, –8) and (2, 7) y = –5x + 17