1.2.2 Graphing Lines

Question 1

Graphing Lines

Answer 1

• A graph is a way of illustrating a set of ordered pairs. One of the easiest objects to graph is the line. Lines have direction, but no thickness.
• The slope-intercept form, y = mx + b, and the point-slope form, (y – y1) = m(x – x1), are two means of describing lines.
• When writing the equation of a line, the point-slope form is easier to use than the slope-intercept form because you can use any point.

Question 2

slope-intercept form

Answer 2

• You can describe a line by an equation that relates the
  x-values and y-values of the points on the line. One form of the equation of a line is the slope-intercept form. This form makes it easy to graph a line because the y-intercept b and the slope m show up distinctly.
• The slope is the pitch of the line. To calculate it, you will need two points on the line. Label their y-coordinates y1 and y2 , respectively, and their x-coordinates x1 and x2, respectively. Divide y2 – y1 by x2 – x1 . If you change the order of the coordinates, you must change the order of both the x-coordinates and the y-coordinates.

Question 3

note

Answer 3

• Here is an example that gives two points and asks you to find the equation of the line passing through them.
• First calculate the slope. You can think of it as the difference of the y-values divided by the difference of the x-values.
• Neither of the points you are given is the y-intercept, so you will have to calculate it. Since the line must pass through (–1, 4), you can substitute those coordinates in place of x and y. This leaves b as the only unknown.
• After you solve for b, substitute its value and the slope into the slope-intercept form.
• If your goal is to write the equation of a line, you may find it easier to use the point-slope form. First, use any two points to calculate the slope. Then use the coordinates of any point on the graph to arrive at the equation of the line.

Question 4

Write the equation of the line through the points (−1, 3) and (3, 1) in point-slope form.

Answer 4

(y-1) = -1/2 (x-3)

Question 5

Joey the mountain climber is hiking up a mountain with slope 2/3. Using his altimeter he finds that he is gaining altitude at a rate of 6000 feet/hour. How fast is he hiking?

Answer 5

10817 feet/hour

Question 6

What is the slope of the line defined by 2x + 3y − 4 = 0?

Answer 6

m = −2/3

Question 7

Find the slope of the line passing through the points (−2, 3) and (4, −5).

Answer 7

−4/3

Question 8

What is the slope of the line described by the equation 5x − 3y + 10 = 0?

Answer 8

5/3

Question 9

What is the y-intercept of the line defined by 2x + 3y − 4 = 0?

Answer 9

b = 4/3

Question 10

Which of the following is the graph of the line y = −3x − 1?

Answer 10

• passes through -1 and increases negatively with steep slope towards quadrant 4
• graph 1

Question 11

Which equation represents a line that is perpendicular to the given graph and passes through the origin?

Answer 11

y = -1/2x

Question 12

What is the slope of this line segment?

Answer 12

m = 5/6

Question 13

Write the equation of the line that passes through the point (1, −2) and is parallel to the line −6x + 3y + 48 = 0 in point-slope form.

Answer 13

( y + 2) = 2 (x − 1)

Question 14

Find the value of a so that the slope of the line passing through the points (1, 4) and (a, a) is 1/4.

Answer 14

None of the above.