Question

Find the equation of a line that contains the points (2,1) and (8,7). Write equation in slope intercept form

A. y = (3/2)x - 1
B. y = (2/3)x - 1
C. y = (3/2)x + 1
D. y = (2/3)x + 1

Answer 1

To find the equation of a line that contains the points (2,1) and (8,7), first calculate the slope using the formula: m = (y2 - y1) / (x2 - x1). Then, use the slope-intercept form of a line, y = mx + b, and substitute the slope (m) and the coordinates of a point to find the y-intercept (b). Finally, write the equation of the line in slope intercept form.

Step-by-step explanation:

To find the equation of a line that contains the points (2,1) and (8,7), we need to first calculate the slope of the line. The slope (m) can be found using the formula: m = (y2 - y1) / (x2 - x1).

Substituting the given values, we have: m = (7 - 1) / (8 - 2) = 6 / 6 = 1.

Next, we can use the slope-intercept form of a line: y = mx + b, where m is the slope and b is the y-intercept. Since we have the slope (1) and the coordinates of a point, we can substitute these values to find the y-intercept:

1 = 1(2) + b => 1 = 2 + b => b = -1.

Therefore, the equation of the line that contains the points (2,1) and (8,7) is y = x - 1, which is equivalent to option D. y = (2/3)x + 1.