Given the points (4,5) and (2.9) what is the equation of the line that goes through both points.

Answer: y = -2x + 13.

Step-by-step explanation:

To find the equation of a line that passes through the points (4,5) and (2,9), we can follow these steps:

1. First, let's determine the slope of the line using the formula: slope (m) = (change in y) / (change in x). We can choose any point as (x1, y1) and the other point as (x2, y2) to calculate the slope.

Using (4,5) as (x1, y1) and (2,9) as (x2, y2):

slope (m) = (5 - 9) / (4 - 2) = -4 / 2 = -2

2. Now that we have the slope (-2), we can use the point-slope form of a line to find the equation. The point-slope form is given by: y - y1 = m(x - x1), where (x1, y1) is one of the given points and m is the slope.

Using (4,5) as (x1, y1) and -2 as the slope (m):

y - 5 = -2(x - 4)

3. Simplifying the equation further, we get:

y - 5 = -2x + 8

4. To obtain the equation in slope-intercept form, we can isolate y by adding 5 to both sides:

y = -2x + 8 + 5

y = -2x + 13

Therefore, the equation of the line that passes through the points (4,5) and (2,9) is y = -2x + 13.

Final answer:

The equation of the line that passes through the points (4,5) and (2,9) is y = x + 1.

Explanation:

To find the equation of the line that goes through the two given points (4,5) and (2,9), we can use the slope-intercept form of a linear equation, y = mx + b.

First, we need to calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the values from the points, we get:

m = (9 - 5) / (2 - 4) = -2 / -2 = 1.

Next, we can substitute the slope and one of the given points into the equation to solve for the y-intercept (b).

Using the point (4,5):

5 = (1)(4) + b

b = 5 - 4 = 1.

Therefore, the equation of the line is y = x + 1.

Learn more about Line equation here:

brainly.com/question/21511618

#SPJ11