Question

Which equation represents the line that passes through (−6,7) and (−3,6)?

a. y=x+9
b. y=−x+9
c. y=x+5
d. y=−x+5

Answer 1

The equation that represents the line passing through (-6,7) and (-3,6) is y = x + 5.

Step-by-step explanation:

The equation that represents the line passing through (-6,7) and (-3,6) is y = x + 5.

To find the equation of a line passing through two points, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.

First, we need to find the slope of the line using the formula:

slope (m) = (y2 - y1) / (x2 - x1)

Plugging in the values from the given points, we get:

slope (m) = (6 - 7) / (-3 - (-6))

slope (m) = -1 / 3

Next, we can choose one of the given points (either (-6,7) or (-3,6)) to substitute into the equation y = mx + b to solve for the y-intercept (b).

Using the point (-6, 7), we can plug in the values of x, y, and m into the equation:

7 = (-1/3)(-6) + b

7 = 2 + b

b = 7 - 2

b = 5

Therefore, the equation of the line passing through (-6,7) and (-3,6) is y = x + 5.