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