$$ \\frac{7 - 3}{6 - 2} = \\frac{4}{4} = 1 $$

$$ \\frac{6 - 2}{4 - 1} = \\frac{4}{3} $$

$$ \\frac{y_2$ - y_1$}{x_2$ - x_1$} $$

Question 1

Given the formula for the slope of a line:

$$ \text{slope} = \frac{y_2$ - y_1$}{x_2$ - x_1$}

If a $$line passes through the points $$(2, 3)$$ and $$(6, 7)$$, what is the slope of the line?

Accepted Answer

$$ \frac{7 - 3}{6 - 2} = \frac{4}{4} = 1 $$

Question 2

If the slope of a line is negative, which of the following best describes the direction of the line on a standard Cartesian plane?

Accepted Answer

The line falls as it moves from left to right.

Question 3

A line has a slope of $$ \frac{1}{2} . If $$the line passes through the point $$(2, 1)$$, what is the equation of the line in slope-intercept form?

Accepted Answer

Question 4

Which of the following lines has the steepest slope?

Accepted Answer

A line with a slope of $$2$$

Question 5

If the slope of a line is $$0$$, what does the line look like on a graph?

Accepted Answer

It is a horizontal line.

Question 6

Given two points $$(1, 2)$$ and $$(4, 6)$$, calculate the slope using the formula $$ \frac{y_2$ - y_1$}{x_2$ - x_1$} .$$

Accepted Answer

$$ \frac{6 - 2}{4 - 1} = \frac{4}{3} $$

Question 7

If a line passes through the points $$(0, 0)$$ and $$(3, 9)$$, what is the slope?

Accepted Answer

$$ \frac{9 - 0}{3 - 0} = 3 $$

Question 8

Which of the following best represents the meaning of 'rise over run' in the context of the slope of a line?

Accepted Answer

The change in the vertical axis divided by the change in the horizontal axis.

Question 9

A line has a slope of $$-1. If it $$passes through the point $$(2, 4)$$, what is the equation of the line in slope-intercept form?

Accepted Answer

$$ y = -x + 6 $$

Question 10

If the slope of a line is undefined, what does the line look like?

Accepted Answer

It is a vertical line.

Question 11

Suppose a line passes through the points $$(5, 2)$$ and $$(5, 8). $$What is the slope of this line?

Accepted Answer

Undefined

Question 12

If a line has a slope of $$0.5$$, and you move 4 units to the right along the x-axis, how many units do you move up along the y-axis?

Accepted Answer

2

Question 13

Which of the following is the correct formula for the slope of a line passing through points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$ \frac{y_2$ - y_1$}{x_2$ - x_1$} $$

Question 14

A line passes through $$(1, 1)$$ and $$(3, 5). $$What is the slope?

Accepted Answer

$$ \frac{5 - 1}{3 - 1} = 2 $$

Question 15

If a line has a slope of $$1$$, which of the following points does NOT lie on the line $$y = x + 2$$?

Accepted Answer

$$(3, 5)$$

Question 16

If the slope of a line is $$0$$, and it passes through the point $$(4, 7)$$, what is the equation of the line?

Accepted Answer

$$ y = 7 $$

Understanding the Slope of Linear Graphs

스터디 가이드 - 연습 문제