Question

Write an equation for the line (0, 7) and (5, 5)

Answer 1

To find the equation of the line through the points (0, 7) and (5, 5), we can use the slope-intercept form of the equation of a line, which is y = mx + b, where m represents the slope and b represents the y-intercept.

First, let's find the slope (m) of the line using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) = (0, 7) and (x2, y2) = (5, 5).

m = (5 - 7) / (5 - 0)
m = -2 / 5

Now that we have the slope (m), we can plug it in along with one of the points (x, y) on the line into the slope-intercept form (y = mx + b) to find the y-intercept (b).

Using the point (0, 7):
7 = (-2/5)(0) + b
7 = b

Therefore, the equation of the line with slope -2/5 and passing through the point (0, 7) is:

y = (-2/5)x + 7