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Write an equation of the line that passes through the points. (2,5),(6,4)

Short Answer

Expert verified
The equation of the line that passes through the points (2,5) and (6,4) is y = -1/4x + 6

Step by step solution

01

Calculate the slope

Use two points from the line to determine the slope. These points are (2,5) and (6,4). Calculate the slope (m) using the formula m = (y2-y1) / (x2-x1). Substitute the corresponding values into the formula to get m = (4 - 5) / (6 - 2) = -1/4.
02

Calculate the y-intercept

Substitute the calculated slope and any point, for instance (2,5), into the formula y = mx + b to solve for the y-intercept (b). Hence, the equation becomes 5 = -1/4 * 2 + b, which simplifies to b = 6 after solving.
03

Write the equation of the line

Substitute the slope and y-intercept values into the line equation y = mx + b to get y = -1/4x + 6

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