Earlier in this chapter we have expressed linear equations using the standard form Ax + By = C and also y= mx +b. Now we're going to focus on the slope-intercept form y = mx + b. In the slope-intercept form you use the slope of the line and the y-intercept to express the linear function. $$y=mx+b$$ Where m is the slope and b is the y-intercept. Example
Graph the equation $$y-2x=1$$ rewrite in slope-intercept form $$y=2x+1$$ Identify the slope and the y-intercept m = 2 and b = 1 Plot the point corresponding to the y-intercept, (0,1) The m-value, the slope, tells us that for each step to the right on the x-axis we move 2 steps upwards on the y-axis (since m = 2) And once you have your second point you can just draw a line through the two points and extend it in both directions. You can check to see that the line you've drawn is the correct one by substituting the coordinates of the second point into the original equation. If the equation holds true than the second point is correct. Our second point = (1, 3) $$y-2x=1$$ $$3-2\cdot 1=3-2=1$$ Our second point is a solution to the equation i.e. the line we drew is correct. A line that passes through the origin has a y-intersect of zero, b = 0, and represents a direct variation. $$y=mx$$ In a direct variation the nonzero number m is called the constant of variation. You can name a function, f by using the function notion $$f\left ( x \right )=mx+b$$ f(x) is another name for y and is read as "the value of f at x" or "f of x". You can use other letters than f to name functions. A group of functions that have similar characteristics are called a family of functions. All functions that can be written on the form f(x) = mx + b belong to the family of linear functions. The most basic function in a family of functions is called the parent function. The parent function of all linear functions is $$f\left ( x \right )=x$$ Video lessonGraph y = 3x - 2 Friday, 11/1/13 - Exploring the Effects of Changing m and b in y=mx+b Form effects_of_changing_slope_and_y-intercept_class_notes_key.pdf Download File Monday, 11/4/13 - Changing m (slope) and b(y-intercept) : finish Friday's packet Tuesday, 11/5/13 - Graphing from y= mx + b; Homework complete #1-6 graphing_-given_slope_and_y-intercept_class_notes.docx Download File Wednesday, 11/6/13 Graphing from Slope Intercept Form using m and b (Finish Class Notes from yesterday); Thursday, 11/7/13 - Converting equations from Standard form to Slope-Intercept form and Graph conversion_of_standard-graphing_classnotes_day_1_key.pdf Download File Friday, 11/8/13 - Convert and Graph Day 2 Monday, 11/11/13 - Graphing using X and Y Intercepts
Tuesday, 11/12/13 - Graphing with Point-Slope Form; graphing review handout due Friday graphing_a_line_given_slope_and_a_point_activity_key.pdf Download File graphing_a_line_given_slope_and_a_point-homework_key.pdf Download File Wednesday, 11/13/13 - Complete yesterday's lesson - Graphing using Point-Slope Form and took notes on various ways to find slope finding_slope_from_2_points-4_methods_-interactive_notebook.pdf Download File Thursday, 11/14/13 - Finding slope from two points (using formula and on calculator) finding_slope_given_two_points_activity-class_notes.pdf Download File Friday, 11/15/13 - Unit 4: Quiz; Finding slope from graphs (review) Monday, 11/18/13-Finding Slope from Tables Tuesday, 11/19/13 - Writing Slope-Intercept Equations Wednesday, 11/20/13 -
Writing Point-Slope Equations Thursday, 11/21/13 - Writing Equations Given 2 Points Friday, 11/21/13 - Graphing a Design using equations and domain Monday, 12/2/13 - family of Lines Applications (effects of changing m and b in y=mx+b) Tuesday, 12/3/13 - REVIEW DAY 1: Four Square Finding Slope/ Writing Equations from 2 pts,tables,graphs, and situations Wednesday, 12/4/13 - REVIEW DAY 2: Unit 4 CUA test review How do you graph slope and ySteps for graphing an equation using the slope and y-intercept:. Find the y-intercept = b of the equation y = mx + b.. Plot the y-intercept. The point will be (0, b).. Find the slope=m of the equation y = mx + b.. Make a single step, using the rise and run from the slope. ... . Connect those two points with your line.. How is the yWhen a linear equation is written in slope-intercept form (y=mx+b), the slope is represented by the variable m. It is the coefficient to x in the equation. The y-intercept is the constant, represented by the variable b.
|