Question

Write an equation in slope-intercept form for the line that passes through (1,9) and (3,5).

A) y = -2x + 11
B) y = -12x + 11
C) y = -2x + 111
D) y = 2x + 11

Answer 1

The equation of the line in slope-intercept form that passes through the points (1,9) and (3,5) is found by calculating the slope (-2) and using one point to solve for the y-intercept (11). The equation is y = -2x + 11, so the correct answer is A) y = -2x + 11.

Step-by-step explanation:

To find the equation of the line in slope-intercept form (which is y = mx + b), we need to determine the slope (m) and the y-intercept (b). The slope of a line passing through two points ((x1, y1) and (x2, y2)) can be found using the formula m = (y2 - y1) / (x2 - x1). For the points given (1, 9) and (3, 5), the slope, m, is calculated as follows:

m = (5 - 9) / (3 - 1) = -4 / 2 = -2

Next, use one of the points to solve for b by plugging the slope and the coordinates of the point into the slope-intercept equation:

9 = (-2)(1) + b

So, b = 9 + 2 = 11.

Therefore, the equation of the line is:

y = -2x + 11

Hence, the correct answer is A) y = -2x + 11.