Can you show me how to do this and give me the final answer please. need help

Find the equation of the line containing the given pair of points.

(2,4) and (6,5)

also need help with this

Find an equation of the line having the given slope and containing the given point

m=-3(1,2)

the first one is the answer y=1/4x+7/2

for the second one is the answer y=-3x+5

correct on both.

To find the equation of a line containing two given points, you can use the slope-intercept form of a linear equation, which is y = mx + b. Here are the steps to find the equation:

Step 1: Find the slope (m)
The slope (m) represents the rate at which the line is rising or falling. It can be calculated using the formula:
m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two given points.

In this case, the given points are (2,4) and (6,5), so we have:
m = (5 - 4) / (6 - 2) = 1 / 4

Step 2: Find the y-intercept (b)
The y-intercept (b) is the point where the line intersects the y-axis. To find it, you can use one of the given points and substitute its coordinates (x, y) into the slope-intercept form of the equation (y = mx + b). Then solve for b.

Let's use the point (2,4):
4 = (1/4)(2) + b
4 = 1/2 + b
b = 4 - 1/2
b = 7/2 or 3.5

Step 3: Write the equation
Now that you have the slope (m) and the y-intercept (b), you can write the equation. Using the slope-intercept form (y = mx + b), substitute the values of m and b:
y = (1/4)x + 3.5

So, the equation of the line containing the points (2,4) and (6,5) is y = (1/4)x + 3.5.