M is the x. A charity organization had to sell 18 tickets to their fundraiser just to cover necessary production costs. Let y represent the net profit in dollars when they have sold x tickets. Which of the. Can someone please check my work?? The bigger the number the slope is in the equation, what do you notice happens to the graph?
When the slope, m, gets bigger the line will become steeper. Write each equation in slope-intercept form of the equation of a line. Underline the slope and circle the y-intercept in each equation.
You can view more similar questions or ask a new question. Similar Questions Algebra 1. This is the cost of rent, insurance, equipment, advertising, and other items that must be paid regularly.
The variable cost depends on the number of units produced. It is for the material and labor needed to produce each item. Stella has a home business selling gourmet pizzas. The equation models the relation between her weekly cost, C , in dollars and the number of pizzas, p , that she sells.
Sam drives a delivery van. The equation models the relation between his weekly cost, C , in dollars and the number of miles, m , that he drives. Loreen has a calligraphy business. The equation models the relation between her weekly cost, C , in dollars and the number of wedding invitations, n , that she writes. The slope of a line indicates how steep the line is and whether it rises or falls as we read it from left to right. Two lines that have the same slope are called parallel lines.
Parallel lines never intersect. We say this more formally in terms of the rectangular coordinate system.
Two lines that have the same slope and different y -intercepts are called parallel lines. What about vertical lines? We say that vertical lines that have different x -intercepts are parallel.
Parallel Lines Parallel lines are lines in the same plane that do not intersect. The first equation is already in slope—intercept form:. We solve the second equation for :. Notice the lines look parallel. What is the slope of each line? What is the y -intercept of each line?
The slopes of the lines are the same and the y -intercept of each line is different. So we know these lines are parallel. Since parallel lines have the same slope and different y -intercepts, we can now just look at the slope—intercept form of the equations of lines and decide if the lines are parallel. Use slopes and y -intercepts to determine if the lines and are parallel.
The lines have the same slope and different y -intercepts and so they are parallel. You may want to graph the lines to confirm whether they are parallel. Use slopes and y -intercepts to determine if the lines are parallel. There is another way you can look at this example. If you recognize right away from the equations that these are horizontal lines, you know their slopes are both 0. Since the horizontal lines cross the y -axis at and at , we know the y -intercepts are and.
Since there is no , the equations cannot be put in slope—intercept form. But we recognize them as equations of vertical lines. Their x -intercepts are and. Since their x -intercepts are different, the vertical lines are parallel. You may want to graph these lines, too, to see what they look like. The lines have the same slope, but they also have the same y -intercepts. Their equations represent the same line.
They are not parallel; they are the same line. These lines lie in the same plane and intersect in right angles. We call these lines perpendicular. What do you notice about the slopes of these two lines? As we read from left to right, the line rises, so its slope is positive. The line drops from left to right, so it has a negative slope. Does it make sense to you that the slopes of two perpendicular lines will have opposite signs? If we look at the slope of the first line, , and the slope of the second line, , we can see that they are negative reciprocals of each other.
If we multiply them, their product is. This is always true for perpendicular lines and leads us to this definition. Perpendicular lines are lines in the same plane that form a right angle. If are the slopes of two perpendicular lines, then:.
Determine the slope and the y -intercept of the given graph. Determine the slope, given two points. A roof drops 4 feet for every 12 feet forward. Determine the slope of the roof. A road drops feet for every 5, feet forward. Determine the slope of the road. The following graph gives the US population of persons 65 years old and over.
At what rate did this population increase from to ? The following graph gives total consumer credit outstanding in the United States. At what rate did consumer credit increase from to ?
Determine the rate at which the van depreciates in value. Determine the rate at which the copy machine depreciates in value. Express the given linear equation in slope-intercept form and identify the slope and y -intercept. Graph the line given the slope and the y -intercept. Graph using the slope and y -intercept. Name three methods for graphing lines. Discuss the pros and cons of each method. Choose a linear equation and graph it three different ways. Scan the work and share it on the discussion board.
Why do we use the letter m for slope? How are equivalent fractions useful when working with slopes? Can we graph a line knowing only its slope?
What strategies for graphing lines should be brought to an exam? Previous Section. Table of Contents. Next Section. Find the slope of the line through the points 6,2 and 3,4.
Possible Answers:. Correct answer:. Explanation : The equation for slope is. The coefficient is 0. What is the slope of the line containing the points 7,12 and 91, Explanation : To find the slope of a line you must first assign variables to each point. Then we plug in our points for and the example looks like Then we perform the necessary subtraction and division to find an answer of.
Explanation :. Which of the following is an example of an equation written in slope-intercept form? Explanation : Slope intercept form is , where is the slope and is the y-intercept.
If 1,2 and 4,6 are on the same line, what is the slope of the line? The equation of a line is: What is the slope of the line? Explanation : Solve the equation for where is the slope of the line:. Explanation : The slope is the rise over the run. Explanation : You can rearrange to get an equation resembling the formula by isolating the. Copyright Notice. View Algebra Tutors.
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