If we know the equation of a line, we can use what we know about slope to write the equation of a line that is either parallel or perpendicular to the given line.
We know that the slope of the line formed by the function is 3. We also know that the y- intercept is 0, 1. Any other line with a slope of 3 will be parallel to f x. So the lines formed by all of the following functions will be parallel to f x. Suppose then we want to write the equation of a line that is parallel to f and passes through the point 1, 7. We already know that the slope is 3. We just need to determine which value for b will give the correct line.
We can begin with the point-slope form of an equation for a line, and then rewrite it in the slope-intercept form. The slope of the given line is 3. We can confirm that the two lines are parallel by graphing them. Figure 22 shows that the two lines will never intersect. We can use a very similar process to write the equation for a line perpendicular to a given line.
Instead of using the same slope, however, we use the negative reciprocal of the given slope. Determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither.
You can view more similar questions or ask a new question. Similar Questions geometry Here is question one to the parallel and perpendicular lines unit test and I really need the answers on them so I can pass this class so anyone please help! Geometry 1Slope and the properties of perpendicular and parallel lines can be used to confirm that a polygon is a specific type of quadrilateral.
List at least two math parallel and perpendicular lines Determine an equation of each of the following lines. The perpendicular slope is. So the equation of the perpendicular line is. First, put the equation of the line given into slope-intercept form by solving for y. Line m passes through the points 1, 4 and 5, 2. If line p is perpendicular to m, then which of the following could represent the equation for p?
Since line p is perpendicular to line m , this means that the products of the slopes of p and m must be — So we must choose the equation that has a slope of 2. What is the equation for the line that is perpendicular to through point? The slope of the given line is and the perpendicular slope is.
We can use the given point and the new slope to find the perpendicular equation. Plug in the slope and the given coordinates to solve for the y-intercept. Using this y-intercept in slope-intercept form, we get out final equation:. Which line below is perpendicular to? For this particular problem, we must first manipulate our initial equation into a more easily recognizable and useful form: slope-intercept form or. According to our formula, our slope for the original line is.
We are looking for an answer that has a perpendicular slope, or an opposite reciprocal. The opposite reciprocal of is. Flip the original and multiply it by. Our answer will have a slope of. Search the answer choices for in the position of the equation. As an aside, the negative reciprocal of 4 is. This does not apply to the above problem, but should be understood to tackle certain permutations of this problem type where the original slope is an integer.
If a line has an equation of , what is the slope of a line that is perpendicular to the line? The equation is used to convert temperatures, , on the Celsius scale to temperatures, , on the Fahrenheit scale. Even though this equation uses and , it is still in slope—intercept form. The slope, , means that the temperature Fahrenheit F increases 9 degrees when the temperature Celsius C increases 5 degrees. The F -intercept means that when the temperature is on the Celsius scale, it is on the Fahrenheit scale.
Start at the F -intercept then count out the rise of 9 and the run of 5 to get a second point. The equation is used to estimate the temperature in degrees Fahrenheit, T , based on the number of cricket chirps, n , in one minute. The cost of running some types business has two components—a fixed cost and a variable cost.
The fixed cost is always the same regardless of how many units are produced. 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?
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