WRITE LINEAR EQUATIONS IN POINT-SLOPE FORM

December 4, 2013

Pages 302-305

Checking 5.2

4.

6.

8. or 9.5

12.

14.

16. or

Checking 5.2

24.

26.

28.

55. -4

56. 1 in.

Write the number correct out of 11.

Given a point and the slope.

Step 1: Plot point

Step 2: Use the slope to move from point to another point.

Step 3: Draw the line connecting the two points.

*Moving points with slope:

up or down, then move right

1. Write an equation in point-slope form of the line

that passes through the point (4, –3) and has a slope of 2.

y – y1 = m (x – x1) Write point-slope form.

y + 3 = 2 (x – 4) Substitute 2 for m, 4 for x1, and –3 for y1.

y – y1 = m (x – x1) Write point-slope form.

y – 4 = –2 (x +1) Substitute – 2 for m, 4 for y, and –1 for x.

2. Write an equation in point-slope form of the line that passes through the point (– 1, 4) and has a slope of – 2 .

SOLUTION

Because the equation is in point-slope form, you know that the line has a slope of and passes through the point (3, –2).

2 3

Plot the point (3, – 2). Find a second

point on the line using the slope.

Draw a line through both points.

y + 2 = (x – 3).2 3

3. Graph the equation.

y – 1 = (x – 2)–4. Graph the equation.

SOLUTION

Because the equation is in point-slope form, you know that the line has a slope of –1 and passes through the point (2, 1).

Plot the point (2, 1). Find a second point on the line using the slope. Draw a line through both points.

5. Write an equation in point-slope form of the line

shown.

SOLUTION

STEP 1

= y1 – y2

x1 – x2

m = 3 –1– 1 –1

=2

– 2= – 1

Find the slope of the line.

Method 1 Method 2

Use (– 1, 3). Use (1, 1).y – y1 = m(x – x1) y – y1 = m(x – x1)

y – 3 = – (x +1) y – 1 = – (x – 1)

STEP 2Write the equation in point-slope form. You can us either given point.

CHECK

Check that the equations are equivalent by writing them in slope-intercept form.

y – 3 = –x – 1y = –x + 2

y – 1 = –x + 1y = –x + 2

STEP 1

= y2 – y1

x2 – x4

m = 4 –3 4 –2

=1

2

Find the slope of the line.

6. Write an equation in point-slope form of the line that passes through the points (2, 3) and (4, 4).

Method 1 Method 2

Use (2, 3) Use (4, 4)y – y1 = m(x – x1) y – y1 = m(x – x1)

STEP 2Write the equation in point-slope form. You can us either given point.

y – 3 = (x – 2)1

2y – 4 = (x – 4)

1 2

HOMEWORK

Worksheet P 5.3