Equations of Lines in Coordinate Geometry

Show your work for each problem.

1.
What is the slope in the equation ?
1. a)
2. b)
3. c)
4. d)
Answer:
In , the slope is (the coefficient of ) and the y-intercept is .
2.
What is the y-intercept in the equation ?
Answer: 7
In , the y-intercept is . This is where the line crosses the y-axis (when ).
3.
Which equation represents a line with slope and y-intercept ?
1. a)
2. b)
3. c)
4. d)
Answer:
With slope and y-intercept , the equation is .
4.
Calculate the slope of the line passing through and .
Answer: 2
Slope .
5.
What form is the equation ?
1. a)Quadratic form
2. b)Slope-intercept form
3. c)Point-slope form
4. d)Standard form
Answer: Point-slope form
This is point-slope form: , where the point is and slope is .
6.
Write the equation of a line passing through with slope . Express in slope-intercept form.
Answer: y = 2x + 1
1. Write point-slope form: . What number goes in the blank? 3
2. Expand: 6
3. Add 7 to both sides: 1
7.
Calculate the slope of the line passing through and .
Answer: -1
Slope .
8.
Convert to standard form.
1. a)
2. b)
3. c)
4. d)
Answer:
Multiply by 2: . Rearrange: . Multiply by : .
9.
Find the equation of the line through and .
Answer: y = 2x - 3
1. Calculate the slope: 2
2. What is the y-intercept? Look at point . -3
3. Write the equation : y = 2x - 3
10.
A line has equation . At what x-value does it cross the x-axis?
Answer: 3
Set : . So , and . The x-intercept is .
11.
Convert to slope-intercept form.
Answer: y = -3/4x + 3
1. Subtract from both sides: -3x + 12
2. Divide everything by 4. What is the slope? -3/4
3. What is the y-intercept? 3
12.
Find the equation of the line through and .
Answer: y = -2x + 1
1. Calculate the slope: . Simplify the numerator first: -12
2. Now the denominator: 6
3. So the slope is -2
4. Use point : . Expand and find the y-intercept: 1
13.
Which line is parallel to ?
1. a)
2. b)
3. c)
4. d)
Answer:
Parallel lines have equal slopes. The original line has slope , so the parallel line must also have slope . Only has slope .
14.
A line passes through and is perpendicular to . What is the slope of this line?
Answer: -1/2
The original slope is . For perpendicular lines, , so , giving .
15.
A phone plan costs 15 euros per month plus 0.10 euros per minute. Write the equation and find the cost for 200 minutes.
Answer: 35
1. What is the fixed cost (y-intercept)? 15
2. What is the cost per minute (slope)? 0.10
3. Write the equation (fill in slope and y-intercept): C = 0.10m + 15
4. Calculate: 35
16.
The line passes through which point?
1. a)
2. b)
3. c)
4. d)
Answer:
Check : ✓. The point is on the line.