What's the equation of the line containing the given pair of points.
(1,4) and (3,5)
(1,4),(3,5).
Slope = (5-4)/(3-1) = 1/2
(1,4).
Y = mx + b = 4
(1/2)*1 + b = 4
b = 7/2
Eq: Y = x/2 + 7/2.
To find the equation of a line that passes through two given points, you can use the slope-intercept form of a linear equation, which is y = mx + b.
Step 1: Find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Let's use the points (1,4) and (3,5) to find the slope:
m = (5 - 4) / (3 - 1)
m = 1 / 2
m = 0.5
Step 2: Choose any one of the given points (let's take point (1,4)) and substitute the values of x, y, and m into the equation y = mx + b to solve for the y-intercept (b).
4 = 0.5(1) + b
4 = 0.5 + b
b = 4 - 0.5
b = 3.5
Step 3: Plug the values of m and b into the equation y = mx + b.
Therefore, the equation of the line passing through the points (1,4) and (3,5) is:
y = 0.5x + 3.5