Question

Find the equation (in terms of x) of the line through the points (-1,1) and (2,5).

A. y = 2x + 3
B. y = 3x + 2
C. y = x + 4
D. y = 4x + 1

Answer 1

To find the equation of the line through the points (-1,1) and (2,5), we can use the slope-intercept form. By calculating the slope and substituting it into the equation, we find that the equation of the line is y = (4/3)x + 7/3.

Step-by-step explanation:

To find the equation of the line through the points (-1,1) and (2,5), we can use the formula for finding the equation of a line in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept. First, we need to find the slope (m) using the formula: m = (y2 - y1)/(x2 - x1). Substituting the coordinates of the two points: m = (5 - 1)/(2 - (-1)), m = 4/3. Now we can substitute the slope and the coordinates of one of the points into the equation y = mx + b to find the y-intercept (b): 1 = (4/3)(-1) + b, 1 = -4/3 + b, b = 7/3. Therefore, the equation of the line is y = (4/3)x + 7/3, which is equivalent to option A. y = 2x + 3.