What Is the Graph of 3x 5y 15?

3x+5y=15 is the graph of a line in the two-dimensional coordinate system. This line has a slope of 3 and y-intercept of 5. It passes through the points (0,5), (3,0), and (6,-5).

The line 3x+5y=15 is parallel to the line 3x+5y=10. Every point on the line 3x+5y=15 is five units above the line 3x+5y=10. The two lines are parallel because they have the same slope (3). A line is parallel to another line if the two lines have the same slope.

The line 3x+5y=15 is also perpendicular to the line y=3x-5. The two lines are perpendicular because the slopes of the lines are negative reciprocals of each other. The slope of the line 3x+5y=15 is 3 and the slope of the line y=3x-5 is -1/3. The product of the slopes of two perpendicular lines is -1.

The y-intercept of a graph is the point where the line crosses the y-axis. In the case of the graph of 3x 5y 15, the y-intercept is the point (0,3). This is because when x=0, y=3.

The x-coordinates of the point of intersection of the graph of 3x + 5y = 15 are -5 and 3. The y-coordinates of the point of intersection of the graph of 3x + 5y = 15 are -3 and 5.

The equation of the line of symmetry of the graph of 3x + 5y = 15 is the line x = 5. This can be seen by graphing the equation and observing that the line of symmetry divides the graph into two halves that are mirror images of each other. The line of symmetry is therefore the line that intersects the graph at the point (5,0).

There are a few different ways to find the coordinates of the vertex of the graph of 3x 5y 15. One way is to use the algebraic method, which involves solving for the x and y values that make the equation true. Another way is to use the graphing method, which involves plotting the points on a graph and finding the point that is the highest or lowest.

To use the algebraic method, we first need to rewrite the equation in standard form. This can be done by subtracting 15 from both sides of the equation to get 3x 5y = 0. We can then solve for y by dividing both sides by 5 to get y = -(3/5)x. We can plug this value of y back into the original equation to get 3x(-3/5)x + 15 = 0. We can then solve for x by factoring the equation to get x(3x - 15) = 0. This gives us two values for x, 0 and 5. We can plug these values back into the original equation to get y = 0 and y = 3, respectively. Therefore, the coordinates of the vertex are (5, 3).

To use the graphing method, we first need to plot the points on a graph. We can do this by substituting values for x into the equation to get corresponding values for y. For example, if we let x = 0, then we get y = 15. If we let x = 1, then we get y = 20. We can continue this until we have a few points plotted on the graph. Once we have a few points, we can look for the point that is the highest or lowest. In this case, the highest point is (5, 3), which is the same as the vertex we found using the algebraic method.

Assuming you are referring to the graph of y = 3x + 5:

The domain of this graph is all real numbers. This is because the equation y = 3x + 5 is a line equation, and all line equations have an infinite domain.

The range of the graph of 3x 5y 15 is the set of all possible values of y that can be obtained by plugging various values of x into the equation. In other words, it is the set of all possible values of y that can be obtained by solving for y in the equation 3x 5y 15. To find the range, we first need to determine what values of y can be obtained when x is equal to 0, 1, 2, and so on. When x is equal to 0, we have 3(0) 5y 15, which Simplifying, we get 5y 15. Solving for y, we get y 3. This means that when x is equal to 0, the value of y is always going to be 3. When x is equal to 1, we have 3(1) 5y 15, which Simplifying, we get 5y 12. Solving for y, we get y 2.4. This means that when x is equal to 1, the value of y is always going to be 2.4. When x is equal to 2, we have 3(2) 5y 15, which Simplifying, we get 5y 9. Solving for y, we get y 1.8. This means that when x is equal to 2, the value of y is always going to be 1.8. We can continue this process for other values of x, and we will eventually see that the range of the graph of 3x 5y 15 is the set of all real numbers greater than or equal to 3.

In mathematics, an asymptote (/ ˈ æ s ɪ m p t oʊ t /) is a line that curves toward or away from a given curve as one or the other of the variables goes to infinity. More precisely, if f is a function defined on an unbounded interval, not taking the value infinity, and g is a differentiable function defined on a neighborhood of infinity such that

lim x → ∞ f ( x ) = lim x → ∞ g ( x )

then g is an asymptote of f. The word asymptote is derived from the Greek ἀσύμπτωτος (asumptōtos), meaning "not falling together", from ἀ- (a-, meaning "without"), σύν (sun-, meaning "with"), and πτωτ-ός (-otos, meaning "falling"). The term was introduced by Apollonius of Perga in his work, Peri tēs asymptōtōn ("On Asymptotes"), defining an asymptote as a line that cuts all other lines parallel to it at a given angle.

In mathematics, the graph of a linear equation is a straight line. The graph of 3x + 5y = 15 is a straight line because it is a linear equation. The slope of this line is 3 and the y-intercept is 5. The equation y = 3x + 5 is the equation of a line that is parallel to the line 3x + 5y = 15. The equation y = 3x + 5 is the equation of a line that is perpendicular to the line 3x + 5y = 15. The point (3, 5) is on the line 3x + 5y = 15. The point (5, 3) is on the line y = 3x + 5.