Chapter 4 4-7 Point slope Form

Objectives Graph a line and write a linear equation using point-slope form. Write a linear equation given two points.

Slope formula If you know the slope and any point on the line, you can write an equation of the line by using the slope formula. For example, suppose a line has a slope of 3 and contains (2, 1) . Let (x, y) be any other point on the line.

Slope formula

Point-slope formula

Example#1 Write an equation in point slope form for the line with the given slope that contains the given point.

Example #2 Write an equation in point slope form for the line with the given slope that contains the given point. slope = 1; (–1, –4)

Example#3 Write an equation in point slope form for the line with the given slope that contains the given point.

Student guided practice Do problems 1-3 in your book page 279.

Point-slope form In previous lessons, you graphed a line given its equation in slope-intercept form. You can also graph a line when given its equation in point-slope form. Start by using the equation to identify a point on the line. Then use the slope of the line to identify a second point.

Example#4 Graph the line described by the equation. y – 1 = 2(x – 3) Solution: y – 1 = 2(x – 3) is in the form y – y1= m(x – x1). The line contains the point (3, 1).

Solution Example#4 Step 1 Plot (3, 1). Step 2 Count 2 units up and 1 unit right and plot another point. Step 3 Draw the line connecting the two points.

Example#5 Graph the line described by the equation.

Solution to Example#5 Step 1 Plot (–2, 4). Step 2 Count 3 units up and 4 units right and plot another point. Step 3 Draw the line connecting the two points.

Example#6 Graph the line described by the equation. y + 3 = 0(x – 4)

Solution to example#6 Step 1 Plot (4, –3). Step 2 There slope is 0. Every value of x will be at y = –3. Step 3 Draw the line connecting the points.

Student guided practice Do problems 4-6 in your book page 279

Exaxmple#7 Write the equation that describes each line in slope-intercept form. Slope = 3, (–1, 4) is on the line. Solution: Step 1 Write the equation in point-slope form: y – y1 = m(x – x1) y – 4 = 3[x – (–1)]

Solution to Example#7 Step 2 Write the equation in slope-intercept form by solving for y. y – 4 = 3(x + 1). y – 4 = 3x + 3Distribute 3 on the right side. + 4 + 4 Add 4 to both sides. y = 3x + 7

Example#8 Write the equation that describes the line in slope-intercept form. (2, –3) and (4, 1)

Example#9 Write the equation that describes the line in slope-intercept form.

Student guided practice Do problems 7-9 in your book page 279

Finding intercepts The points (1, –2) and (3, 10) are on a line . Find the intercepts.

Example#10 The points (2, 15) and (–4, –3) are on a line. Find the intercepts.

Student guided practice Do problems 13 and 14 in your book page 279.

Problem solving application The cost to stain a deck is a linear function of the deck’s area. The cost to stain 100, 250, 400 square feet are shown in the table. Write an equation in slope-intercept form that represents the function. Then find the cost to stain a deck whose area is 75 square feet.

solution

Problem solving application What if…? At a newspaper the costs to place an ad for one week are shown. Write an equation in slope-intercept form that represents this linear function. Then find the cost of an ad that is 21 lines long.

solution

Homework Do evens problems from 23-33 pg. 280

Closure Today we learned how to write equations in slope intercept form. Next class we are going to have a discovery activity to find the line of best fit.

Have a great day