Writing Slope-Intercept Equations
Watch this lecture series and complete the interactive exercises to learn how to write an equation of a line in slope-intercept form.
Writing linear equations word problems - Questions
Answer
The fee for every vertical meter climbed is constant, so we are dealing with a linear relationship.
Let's interpret the meaning of the given information in terms of the line representing this relationship.
The initial fee is . This corresponds to the point , which is also the -intercept.
The total fee for climbing up meters is , which corresponds to the point .
Let's use the slope formula with the points and .
This means that the agency charges a constant fee of per vertical meter climbed.
Now we know the slope of the line is and the -intercept is , so we can write the equation of that line:
Rachel drove at a constant rate, so we are dealing with a linear relationship.
Let's interpret the meaning of the given information in terms of the line representing this relationship.
Rachel drove meters per second. This corresponds to a slope with an absolute value of .
Notice that Rachel is driving closer to the safe zone. So our line is decreasing, which means the slope is .
After seconds of driving, she was meters away from the safe zone. This corresponds to the point .
So the slope of the relationship's line is and the line passes through .
Let's find the -intercept, represented by the point , using the slope formula:
Solving this equation, we get .
Show me the solution.
Now we know the slope of the line is and the -intercept is , so we can write the equation of that line:
Carolina's hourly fee is constant, so we are dealing with a linear relationship.
Let's interpret the meaning of the given information in terms of the line representing this relationship.
Carolina's fee increases at a rate of per hour. This corresponds to a slope of .
Carolina's total fee for a -hour job is . This corresponds to the point .
So the slope of the relationship's line is and the line passes through .
Let's find the -intercept, represented by the point , using the slope formula:
Solving this equation, we get .
Show me the solution.
Now we know the slope of the line is and the -intercept is , so we can write the equation of that line:
Kayden drove at a constant rate, so we are dealing with a linear relationship.
Let's interpret the meaning of the given information in terms of the line representing this relationship.
The initial distance to drive was meters. This corresponds to the point , which is also the -intercept.
There were meters left after seconds, which corresponds to the point .
Let's use the slope formula with the points and .
This means that the distance to the safe zone decreased by meters per second (because Kayden drove at a speed of meters per second).
Now we know the slope of the line is \greenD{-25}−25start color #1fab54, minus, 25, end color #1fab54 and the yyy-intercept is and the -intercept is , so we can write the equation of that line: