Question 1

Which of the following is the point-slope form of the equation of a line with slope $$m = 6$$ passing through the point $$(2, -5)$$?

Accepted Answer

$$y + 5 = 6(x - 2)$$

Question 2

Given two points $$(-2, -1)$$ and $$(-1, -6)$$, what is the slope $$m of $$the line passing through them?

Accepted Answer

$$m = -5$$

Question 3

What is the slope-intercept form of the line passing through $$(2, -5)$$ with slope $$6$$?

Accepted Answer

$$y = 6x - 17$$

Question 4

A line passes through $$(10, 30.0)$$ and $$(20, 32.8). $$What is the slope of this line?

Accepted Answer

$$m = 0.28$$

Question 5

Using the data points $$(10, 30.0)$$ and $$(20, 32.8)$$, what is the slope-intercept form of the equation modeling the median age $$y as a $$function of years $$x$$ after 1970?

Accepted Answer

$$y = 0.28x + 27.2$$

Question 6

If the equation $$y = 0.28x + 27.2$$ models the median age of the U.S. population $$x$$ years after 1970, what is the predicted median age in 2020?

Accepted Answer

$$41.2$$

Question 7

Which of the following best describes the point-slope form of a line?

Accepted Answer

$$y - y_1$ = m(x - x_1$)$$

Question 8

Suppose the median age in 1980 was $$30.0$$ and in 2000 was $$35.3. $$What is the average rate of change in median age per year between 1980 and 2000?

Accepted Answer

$$0.265$$

Question 9

A researcher wants to predict the median age in 2030 using the model $$y = 0.28x + 27.2. $$What value should be used for $$x$$?

Accepted Answer

$$60$$

Question 10

Which of the following statements is true about the line with equation $$y = 0.28x + 27.2$$?

Accepted Answer

The line predicts a steady increase in median age over time.

Question 11

Given the point-slope equation $$y + 1 = -5(x + 2)$$, what is the slope-intercept form?

Accepted Answer

$$y = -5x - 11$$

Question 12

If a line has the equation $$y = mx + b$$ and passes through $$(0, b)$$, what does $$b$$ represent?

Accepted Answer

The $$y-$$intercept

Question 13

A city’s population median age is modeled by $$y = 0.28x + 27.2. If $$the actual median age in 2010 is $$37.4$$, how does the model’s prediction compare?

Accepted Answer

The model underestimates the actual median age.

Question 14

Which of the following is NOT a correct step in converting point-slope form to slope-intercept form?

Accepted Answer

Multiplying both sides by $$x$$

Question 15

If the median age increases by $$0.28$$ years per year, how much will it increase in $$25$$ years?

Accepted Answer

$$7$$

Linear Equations and Inequalities in Two Variables: Point-Slope Form and Applications

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