Algebraically Finiding an Equation of a Line with a Point and Slope.

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Presentation transcript:

Algebraically Finiding an Equation of a Line with a Point and Slope

Algebraically Finding the y-intercept Colleen wants to know how much a chick weighs when it is hatched. Colleen tracked one of her chickens and found it grew steadily by about 5.2 grams each day since it was born. Nine days after it hatched, the chick weighed 98.4 grams. Algebraically determine how much the chick weighed the day it was hatched. Since the growth is constant, the situation in linear: The growth (slope) is 5.2 grams per day The chick weighed 98.4 grams (y) after 9 days (x) The equation now has one distinct variable. Solve it. When the chick was hatched, it was day 0. Thus, we need to find the y-intercept grams

Algebraically Finding a x-Value Now Colleen wants to know when the chicken will weigh 140 grams. Algebraically find the answer. Use the Slope- Intercept form: Substitute 140 for y The equation now has one distinct variable. Solve it. Use the slope and y-intercept to write an equation. 17 Days The 140 grams represents a y value.

Example Algebraically find the equation for a line with a slope of -3, passing through the point (15,-50). Use Slope-Intercept Form: The slope is -3 A point on the graph is x=15 and y=-50 The equation now has one distinct variable. Solve it. Find the y-intercept. Substitute back into Slope- Intercept Form:

Perpendicular Lines A line is perpendicular to another if it meets or crosses at right angles (90°). For instance, a horizontal and a vertical line are perpendicular lines.

Complete the following assuming Line A and Line B are perpendicular. 1.Make Line A have a slope of. 2.What is the slope of Line B (the line perpendicular to Line A)? Slopes of Perpendicular Lines A B A B A B A B

Slopes of Perpendicular Lines Two lines are perpendicular if their slopes are opposite reciprocals of each other. In other words, if the slope of a line is then the perpendicular line has a slope of. Example: What is the slope of a line perpendicular to each equation below.

Example Algebraically find the equation of the line that goes through the point (2,3) and is perpendicular to y = -4x – 2. Use Slope-Intercept Form: The slope is ¼ A point on the graph is x=2 and y=-3 The equation now has one distinct variable. Solve it. Find the y-intercept. Substitute back into Slope- Intercept Form: This y-intercept does not matter.

Example: Parallel Lines Algebraically find the equation of the line that goes through the point (16,4) and is parallel to 3x + 4 y = 8. Use Slope- Intercept Form: The slope is -3/4 A point on the graph is x=16 and y=4 The equation now has one distinct variable. Solve it. Find the y-intercept. Substitute back into Slope-Intercept Form: Since Parallel Lines have the same slope, our new equation also has slope -3/4. (This y- intercept does not matter) Find the Slope