Interpreting Graphs of Linear Equations

What does the slope of a line represent in a graph of a linear equation in two variables?

• The maximum value of the dependent variable

• The rate at which the dependent variable changes with respect to the independent variable

• The intersection point of the line with the y-axis

• The intersection point of the line with the x-axis

Consider a graph of a linear equation showing the relationship between temperature in Celsius and Fahrenheit. If the slope of the line is positive, what does this indicate about the relationship between Celsius and Fahrenheit temperatures?

• As the temperature in Celsius decreases, the Fahrenheit temperature increases

• There is no relationship between Celsius and Fahrenheit temperatures

• As the temperature in Celsius increases, the Fahrenheit temperature decreases

• As the temperature in Celsius increases, the Fahrenheit temperature also increases

What does the y-intercept of a graph of a linear equation represent?

• The rate of change of the dependent variable

• The maximum value of the independent variable

• The value of the dependent variable when the independent variable is zero

• The value of the independent variable when the dependent variable is zero

What does a steeper slope in a graph of a linear equation imply about the relationship between the two variables compared to a shallower slope?

• The variables are unrelated

• The relationship between the variables is weaker

• The relationship between the variables is stronger

• The direction of the relationship between the variables is reversed

If a line in a graph has a slope of 2, what does this mean?

• For every 1 unit increase in the x-axis, the value of y decreases by 2 units

• For every 1 unit increase in the x-axis, the value of y increases by 2 units

• The line crosses the y-axis at the point (0, 2)

• The line crosses the x-axis at the point (2, 0)

If a graph of a linear equation has a slope of -3, how does the dependent variable change as the independent variable increases?

• It increases by 3 units

• It decreases by 3 units

• It remains constant

• It increases by 1/3 unit

In a graph showing the relationship between the number of hours studied and the score on a test, if the line has a steep slope, what does this indicate about the relationship between hours studied and test score?

• There is a weak relationship between hours studied and test score

• There is a strong positive relationship; scores increase significantly with more hours studied

• There is a strong negative relationship; scores decrease with more hours studied

• The number of hours studied has no effect on the test score

If a graph of a linear equation relating the amount of fertilizer used to the height of a plant has a negative slope, what does this tell you?

• Using more fertilizer always decreases the height of the plant

• Using more fertilizer has no effect on the height of the plant

• Using more fertilizer increases the height of the plant

• The relationship between fertilizer use and plant height cannot be determined from the slope alone

In a graph of a linear equation showing the relationship between the amount of sales and profit, if the slope is positive, what does this indicate?

• Profits decrease as sales increase

• Profits increase at a constant rate as sales increase

• Profits remain constant regardless of sales

• Sales have no impact on profits

In the context of a graph representing distance versus time, what does a slope of zero indicate?

• The object is moving at a constant speed

• The object is accelerating

• The object is not moving

• The object is moving at an increasing speed