Q: Which of the following is the correct process to find the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$?

$m = 5cfrac{y_2 - y_1}{x_2 - x_1}$

Question 1

Given the points $(-4, 9)$ and $(1, -1)$, what is the slope $m$ of the line passing through these points?

Accepted Answer

$m = 2$

Question 2

What is the equation of the line passing through $(-4, 9)$ and $(1, -1)$ in point-slope form?

Accepted Answer

$y - 9 = 2(x + 4)$

Question 3

What is the equation of the line passing through $(-4, 9)$ and $(1, -1)$ in slope-intercept form?

Question 4

If a line passes through $(-4, 9)$ and $(1, -1)$, what is the $y$-intercept of the line?

Accepted Answer

$b = -3$

Question 5

Which of the following is the correct process to find the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$?

Accepted Answer

$m =  5cfrac{y_2 - y_1}{x_2 - x_1}$

Question 6

A biologist tracks the migration of a bird and finds its position changes from $(-4, 9)$ km to $(1, -1)$ km over a certain period. What is the average rate of change in the bird's $y$-position per kilometer in $x$?

Accepted Answer

$2$ km per km

Question 7

Given the point-slope form $y - 9 = 2(x + 4)$, which of the following is the equivalent slope-intercept form?

Accepted Answer

$y = 2x - 3$

Question 8

A company’s profit $y$ (in thousands of dollars) depends linearly on the number of units $x$ sold. If the profit is $9$ thousand dollars when $-4$ units are sold (a loss), and $-1$ thousand dollars when $1$ unit is sold, what is the equation relating $y$ and $x$ in slope-intercept form?

Accepted Answer

$y = 2x - 3$

Question 9

Which of the following statements is true about the line passing through $(-4, 9)$ and $(1, -1)$?

Accepted Answer

The line has a positive slope and increases as $x$ increases.

Question 10

If the equation of a line is $y = 2x - 3$, what is the $x$-coordinate where the line crosses the $x$-axis?

Accepted Answer

$x = 1.5$

Equations of a Line: Point-Slope and Slope-Intercept Forms

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