Final answer:
The slope and y-intercept of the line passing through points (3,-1) and (1,4) are -5/2 and -1/2, respectively. Therefore, the equation of the line in slope-intercept form is y = -5/2x - 1/2.
Step-by-step explanation:
To find the equation of a line in slope-intercept form (y = mx + b), we first need to find the slope (m) and y-intercept (b). The slope of a line through two points (x1, y1) and (x2, y2) is given by the formula m = (y2 - y1) / (x2 - x1). Substituting the given points (3,-1) and (1,4) into this formula, we find that m = (4 - (-1)) / (1 - 3) = -5/2. Next, we substitute one of the points and the slope into the equation y = mx + b to find b. Using the point (3,-1), we get -1 = (-5/2)*3 + b, which simplifies to b = -1/2. Therefore, the equation of the line in slope-intercept form is y = -5/2x - 1/2.
Learn more about Slope-intercept form