Point-Slope Form

Show your work for each problem.

1.
What is the point-slope form of a linear equation?
1. a)
2. b)
3. c)
4. d)
Answer:
is point-slope form. is slope-intercept form, and is standard form.
2.
In point-slope form , what does represent?
1. a)The y-intercept
2. b)The y-coordinate
3. c)The slope
4. d)The x-coordinate
Answer: The slope
In point-slope form, represents the slope (rate of change) of the line, while is a specific point on the line.
3.
A line has slope and passes through . Write the equation in point-slope form:
Answer: 4
In point-slope form , we substitute the slope . The equation is .
4.
Convert to slope-intercept form. What is (the y-intercept)?
Answer: -3
becomes . Adding 2: . So .
5.
Write the equation of a line with slope passing through .
Answer: y - 7 = 2(x - 3)
1. What is the slope ? 2
2. What is (the x-coordinate of the point)? 3
3. What is (the y-coordinate of the point)? 7
4. Substitute into . What is the equation? y - 7 = 2(x - 3)
6.
Which equation represents a line through with slope ?
1. a)
2. b)
3. c)
4. d)
Answer:
With point : simplifies to .
7.
Calculate the slope of the line through and .
Answer: 2
8.
Find the equation of the line through and .
Answer: y - 2 = 3(x - 1)
1. Calculate 9
2. Calculate 3
3. What is the slope ? 3
4. Using point , write the equation y - 2 = 3(x - 1)
9.
What is the slope of a line parallel to ?
1. a)
2. b)
3. c)
4. d)
Answer:
Parallel lines have identical slopes. Since has slope , any parallel line also has slope .
10.
What is the slope of a line perpendicular to ? (Express as a fraction if needed)
Answer: -1/2
The slope of is . The perpendicular slope is (negative reciprocal).
11.
Write the equation of a line parallel to that passes through .
Answer: y - 5 = 3(x - 2)
1. What is the slope of ? 3
2. What is the slope of a parallel line? 3
3. Using point , write the point-slope equation y - 5 = 3(x - 2)
12.
Convert to slope-intercept form.
Answer: y = -2x + 7
1. Distribute to -2x + 8
2. Rewrite the equation y + 1 = -2x + 8
3. Subtract 1 from both sides to isolate y = -2x + 7
13.
Which equation represents a line perpendicular to passing through ?
1. a)
2. b)
3. c)
4. d)
Answer:
Perpendicular to gives . Through : .
14.
Convert to slope-intercept form. What is ?
Answer: 8
. Adding 4: . So .
15.
Write the equation of a line perpendicular to that passes through .
Answer: y - 2 = 4(x - 8)
1. What is the slope of the given line? -1/4
2. What is the perpendicular slope? 4
3. Using point , write the equation y - 2 = 4(x - 8)
16.
Find the equation of the line through and .
Answer: y - 5 = -1(x + 3)
1. Calculate -6
2. Calculate 6
3. What is the slope ? -1
4. Using point , write the equation y - 5 = -1(x + 3)
17.
A line passes through and . What is the y-intercept of this line?
Answer: -4
Since the point has , this IS the y-intercept! The line crosses the y-axis at .
18.
The lines and are:
1. a)The same line
2. b)Neither parallel nor perpendicular
3. c)Parallel lines
4. d)Perpendicular lines
Answer: The same line
First equation: . Second: , so . Same equation - same line!