Find the equation of the line that passes through the following two points:(2, 8) and (4, 18)Group of answer choicesy = -5x + 18y = 5x - 10𝑦=15𝑥+385y = 5x - 2𝑦=15𝑥−25y = -5x + 10
Question
Find the equation of the line that passes through the following two points:(2, 8) and (4, 18)Group of answer choicesy = -5x + 18y = 5x - 10𝑦=15𝑥+385y = 5x - 2𝑦=15𝑥−25y = -5x + 10
Solution
To find the equation of the line that passes through two points, we first need to find the slope (m) of the line. The formula for the slope is (y2 - y1) / (x2 - x1).
Given points are (2, 8) and (4, 18). Let's plug these values into the formula:
m = (18 - 8) / (4 - 2) = 10 / 2 = 5
So, the slope of the line is 5.
The general form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept. We already know m = 5. To find b, we can substitute one of the points and the slope into the equation and solve for b. Let's use the point (2, 8):
8 = 5*2 + b 8 = 10 + b b = 8 - 10 = -2
So, the equation of the line that passes through the points (2, 8) and (4, 18) is y = 5x - 2.
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