Forms (Linear Equations)

Question 1

The standard form of an equation of a line.

Answer 1

ax + by = c

Question 2

What is the standard form of an equation useful for?

Answer 2

for solving systems of two linear equations that are expressed in a way that is hard to solve

Question 3

What is the point-slope form?

Answer 3

y - y1 = m(x - x1)

Question 4

What is the point-slope form useful for?

(hint: the name)

Answer 4

for finding the y-intercept on a line (or constant) when you know the slope and a set of points (or x1, y1)

Question 5

What is the two-intercept form?

Answer 5

x/a + y/b = 1

[where a is the x-intercept when (a,0) and b is the y-intercept when (0,b)]

Question 6

What is the slope of a straight line given in two-intercept form?

Answer 6

-b/a

(where b is the y-intercept and a is the x-intercept)

Question 7

When is the two-intercept form useful?

Answer 7

the two-intercept from allows us to see the x- and y- intercepts directly with no rearrangements required; we can use this to plot the line or calculate the slope

Question 8

What is one way to find the coordinates of the x- or y- intercept when one is undetermined?

Answer 8

by substituting 0 for the other intercept in any form of the equation of a straight line

Question 9

What is the slope-intercept form?

Answer 9

y = mx + b

Question 10

How do we find the slope? (general formula)

Answer 10

m = y2 - y1/x2 - x1

(alt: m = rise/run)

Question 11

How do we find the slope? (trig function)

Answer 11

m = tanθ