Write an equation in standard form for a line with an x-intercept of 2 and a y-intercept of 5.

I cannot find any examples of how to do this problem, all of the examples that I have show how to do it with a slope and point. Any help would be great!

Thanks.

You have two points given; they are (0,5) for the y intercept of 5 and (2,0) for the x intercept of 2. Find the slope from those two points and use the slope and point OR solve two simultaneous equations of the y = mx + b type.

x-intercept of 2 means that at

x = 2, y = 0. Note that the line y = 0 is the x-axis.

y-intercept of 5 means that at x = 0,
y = 5. Note that the line x = 0 is the y-axis.

So, you need to find the equation of the line that moves throuh the points (2,0) and (0,5)

You can do that by writing down the general equation of the lign and then solvong for the paramenters by demanding that it moves through these points. However, that's in general an inefficent way to solve the problem.

In this case, it is particularly easy to solve to solve the problem. You know that at x = 2, y = 0. That means that the function must be of the form:

y = A(x-2)

At x = 0, y = 5, so A = -5/2.

To write an equation in standard form for a line with given x-intercept and y-intercept, you can use the fact that the x-intercept occurs at the point (2, 0), and the y-intercept occurs at the point (0, 5).

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

To find the equation of the line, we need to find the values of A, B, and C.

First, let's find the slope of the line using the two given points:

m = (y2 - y1) / (x2 - x1)
= (5 - 0) / (0 - 2)
= 5 / -2
= -5/2

Now, since we have the slope and the y-intercept, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept:

y = (-5/2)x + 5

Next, to write the equation in standard form, we need to clear the fraction.

Multiply both sides of the equation by 2:

2y = -5x + 10

Now, rearrange the equation to have the x and y terms on the left side and the constant term on the right side:

5x + 2y = 10

Therefore, the equation in standard form for the line with an x-intercept of 2 and a y-intercept of 5 is 5x + 2y = 10.

To write the equation of a line in standard form, we need to use two pieces of information: the x-intercept and the y-intercept. The x-intercept occurs when y = 0, and the y-intercept occurs when x = 0.

In this case, given that the x-intercept is 2 and the y-intercept is 5, we know that the line passes through the points (2,0) and (0,5).

To find the equation of the line, we need to calculate the slope (m) first. The slope is equal to the change in y divided by the change in x between two points on the line. So we have:

m = (y2 - y1) / (x2 - x1)
m = (0 - 5) / (2 - 0)
m = -5 / 2

Now that we have the slope, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

Using the point (2,0), we have:

y - 0 = (-5/2)(x - 2)

y = (-5/2)(x - 2)

To convert this equation to standard form, we need to eliminate the fraction. Multiply both sides of the equation by 2 to do that:

2y = -5(x - 2)

2y = -5x + 10

Now, rearrange the equation to get it in the standard form:

5x + 2y = 10

So the equation in standard form for the line with an x-intercept of 2 and a y-intercept of 5 is 5x + 2y = 10.