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?

Accepted Answer

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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