Problem

Question 10) Find the equation of a line in slope-intercept form that passes through the given pairs of points. Show your work for full credit. A line passes through $(1,2)$ and $(5,10) \ldots$ A line passes through $(4,5)$ and $(8,3) \ldots$

Solution

Step 1 :Find the slope of the line that passes through the points (1,2) and (5,10) using the formula m = (y2 - y1) / (x2 - x1). In this case, m = (10 - 2) / (5 - 1) = 2.0

Step 2 :Substitute the slope and one of the points into the equation y = mx + b to find the y-intercept. In this case, 2 = 2*1 + b, so b = 0.0

Step 3 :The equation of the line in slope-intercept form that passes through the points (1,2) and (5,10) is therefore y = 2x + 0, which simplifies to \(\boxed{y = 2x}\)

Step 4 :Find the slope of the line that passes through the points (4,5) and (8,3) using the formula m = (y2 - y1) / (x2 - x1). In this case, m = (3 - 5) / (8 - 4) = -0.5

Step 5 :Substitute the slope and one of the points into the equation y = mx + b to find the y-intercept. In this case, 5 = -0.5*4 + b, so b = 7.0

Step 6 :The equation of the line in slope-intercept form that passes through the points (4,5) and (8,3) is therefore \(\boxed{y = -0.5x + 7}\)

From Solvely APP
Source: https://solvelyapp.com/problems/46264/

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