Final answer:
To determine the equation of the line passing through the points (-1,1) and (1,7), we can use the formula for finding the slope of a line and the point-slope form of the linear equation. The slope between the points is 3, and using the point (-1,1), we can find the equation y = 3x + 4. Converting it to standard form, the equation becomes 3x - y = -4.
Step-by-step explanation:
To determine the equation of the line passing through the points (-1,1) and (1,7), we can use the formula for finding the slope of a line. The slope (m) between two points (x1,y1) and (x2,y2) is given by the formula m = (y2 - y1) / (x2 - x1). Plugging in the values from the given points, we get m = (7 - 1) / (1 - (-1)) = 6 / 2 = 3.
Next, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is one of the given points and m is the slope. Let's use the point (-1,1) and the slope 3 to find the equation. y - 1 = 3(x - (-1)) simplifies to y - 1 = 3(x + 1).
To convert the equation to standard form ax + by = c, we expand it: y - 1 = 3x + 3 becomes y = 3x + 4. Rearranging the equation in the standard form, we get 3x - y = -4. Therefore, the equation of the line passing through the points (-1,1) and (1,7) in standard form is 3x - y = -4.