Question

Line a passes through (-1,1) and (1,3). Line a passes through (-6,3) and (0,6). Line b passes through (3,4) and (0,2). Line b passes through (-5,0) and (7,6). Line c passes through (0,1) and (3,3). Line c passes through (2,1) and (10,-3)

Answer 1

Step-by-s

AI-generated answer

To find the equations of the lines, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope of the line and b represents the y-intercept.

For Line a:

Step 1: Calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points on the line.

m = (3 - 1) / (1 - (-1)) = 2 / 2 = 1

Step 2: Choose one of the given points and substitute its coordinates into the slope-intercept form (y = mx + b) to solve for the y-intercept (b).

Using the point (-1, 1):

1 = 1(-1) + b

1 = -1 + b

b = 2

Therefore, the equation of Line a is y = x + 2.

For Line b:

Step 1: Calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1).

m = (2 - 4) / (0 - 3) = -2 / -3 = 2/3

Step 2: Choose one of the given points and substitute its coordinates into the slope-intercept form (y = mx + b) to solve for the y-intercept (b).

Using the point (3, 4):

4 = (2/3)(3) + b

4 = 2 + b

b = 2

Therefore, the equation of Line b is y = (2/3)x + 2.

For Line c:

Step 1: Calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1).

m = (3 - 1) / (3 - 0) = 2 / 3

Step 2: Choose one of the given points and substitute its coordinates into the slope-intercept form (y = mx + b) to solve for the y-intercept (b).

Using the point (0, 1):

1 = (2/3)(0) + b

1 = b

Therefore, the equation of Line c is y = (2/3)x + 1.

These are the equations of the lines:

Line a: y = x + 2

Line b: y = (2/3)x + 2

Line c: y = (2tep explanation: