Final answer:
To find the equation of the line passing through the points (-1,3) and (2,4), we first calculate the slope using the formula. Then, we use the point-slope form of a linear equation to find the equation of the line. The equation of the line passing through the given points is y = 1 / 3 x + 10 / 3.
Step-by-step explanation:
To find the equation of the line passing through the points (-1,3) and (2,4), we first need to find the slope of the line. The slope can be found using the formula m = (y2-y1)/(x2-x1), where (x1,y1) and (x2,y2) are the coordinates of the two points.
Using the formula, we have m = (4 - 3) / (2 - (-1)) = 1 / 3.
Next, we can use the point-slope form of a linear equation y - y1 = m(x - x1), where (x1,y1) is one of the points on the line.
Using the point (-1,3), we have y - 3 = 1 / 3(x - (-1)). Simplifying this equation, we get y - 3 = 1 / 3(x + 1). Rearranging the equation to slope-intercept form, we have y = 1 / 3 x + 1 / 3 + 9 / 3 = 1 / 3 x + 10 / 3.
Therefore, the equation of the line passing through the points (-1,3) and (2,4) is y = 1 / 3 x + 10 / 3.