10.5 Writing Slope-Intercept Equations of Lines - PowerPoint PPT Presentation

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10.5 Writing Slope-Intercept Equations of Lines. CORD Math Mrs. Spitz Fall 2006. Objectives:. Write a linear equation in slope-intercept form given the slope of a line and the coordinates of a point on the line, and

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10.5 Writing Slope-Intercept Equations of Lines

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10.5 Writing Slope-Intercept Equations of Lines

CORD Math

Mrs. Spitz

Fall 2006

Objectives:

• Write a linear equation in slope-intercept form given the slope of a line and the coordinates of a point on the line, and

• Write a linear equation in slope-intercept form given the coordinates of two points on the line.

Assignment

• Pgs. 421-422 #4-31 all

Application

• The present population of Cedarville is 55,000. If the population increases by 600 people each year, the equation y = 600x + 55,000 can be used to find the population x years from now. Notice that 55,000 is the y-intercept and 600 (the growth per year) is the slope.

Application continued

• In the problem above, the slope and y-intercept were used to write an equation. Other information can also be used to write an equation for a line. In fact, given any one of the three types of information below about a line, you can write an equation for a line.

• The slope and a point on the line

• Two points on a line

• The x- and y-intercepts

Ex. Write an equation of whose slope is 3 that passes through (4, -2).

y = mx + b Use slope-intercept form

y = 3x + b The slope is 3

-2 = 3(4) + b Substitute 4 for x and -2 for y

-2 = 12 + b Solve for b

-14 = b

The slope-intercept form of the equation of the line is y = 3x + (-14) or y = 3x – 14.

Ex. Write an equation of whose slope is 3 that passes through (4, -2).

The slope-intercept form of the equation of the line is y = 3x + (-14) or y = 3x – 14. In standard form:

y = 3x – 14 Slope-intercept form

-3x + y = -14 Subtract x from both sides

3x – y = 14 Multiply by -1 to change the sign of the leading coefficient in front of x.

What about the equation with 2 points?

• Example 2 illustrates a procedure that can be used to write an equation of a line when two points on the line are known.

• Write an equation in slope-intercept form of the line that passes through each pair of points: (-1, 7), (8, -2)

• First determine the slope of the line

Ex. 2 continued

(-1, 7), (8, -2) are the two points. m = -1

y = mx + b slope intercept form

y = -1x + b substitute -1 for m

7 = -1(-1) + b substitute 7 for y and -1 for x

7 = 1 + b Distribute

6 = b Solve for b

Equation of the line is y = -x + 6

Ex. 3: Write an equation of the line that passes through (7.6, 10.8) and (12.2, 93.7). Round values to the nearest thousandth.

y = mx + b

Slope-intercept form

y = 18.022x + b

Substitute 18.022 for slope, m

Substitute 10.8 for y and 7.6 for x

10.8 = 18.022(7.6) + b

Distribute/simplify

10.8 = 136.967 + b

Subtract 136.067 from both sides

-126.167 = b

Equation of the line is y = 18.022x – 126.167

So you could just look at the graph and count, right? Rise over run. You know its negative because of the way it’s facing. So count.

Ex. 4: Write an equation for line PQ whose graph is shown below.

1, 2 , 3 , 4 down

1, 2 , 3 over to the right

-4/3 right?

You could also use the slope formula with the points (0, 4) and (3, 0)

Ex. 4: Write an equation for line PQ whose graph is shown below.

Simply a matter of following the formula from there.

Ex. 4: Write an equation for line PQ whose graph is shown below.

• Points (0, 4) and (3, 0)

y = mx + b

Rewrite the equation as:

Rewrite the equation in standard form as follows: