Question

To find the equation of the line that passes through the points (2, -4) and (-4, 9) in slope-intercept form (y = mx + b), you first need to find the slope (m). The formula for slope (m) is (y2 - y1) / (x2 - x1). Using the points (2, -4) and (-4, 9):

m = (9 - (-4)) / (-4 - 2) = (13) / (-6) = -13/6

Now that you have the slope (m), you can use one of the points and the slope to find the equation. Let's use (2, -4):

-4 = (-13/6)(2) + b

Now, solve for b:

-4 = -26/6 + b
-4 = -13/3 + b

To find b, add 13/3 to both sides:

b = -4 + 13/3
b = -12/3 + 13/3
b = 1/3

So, the equation of the line in slope-intercept form is:

y = (-13/6)x + 1/3

Answer 1

The slope-intercept form of the line passing through the points (2, -4) and (-4, 9) is calculated by first determining the slope (m) and then solving for the y-intercept (b) to arrive at the equation y = (-13/6)x + 1/3.

Step-by-step explanation:

To find the equation of a line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, you first determine the slope using two points (x1, y1) and (x2, y2). The formula for the slope is (y2 - y1) / (x2 - x1). In this case, the slope m = (9 - (-4)) / (-4 - 2) simplifies to -13/6.

Once the slope is found, choose one of the points to solve for the y-intercept (b). With the point (2, -4) and the slope -13/6, you set up the equation -4 = (-13/6)(2) + b, which upon solving gives b = 1/3.

Therefore, the equation in slope-intercept form with the determined slope and y-intercept is y = (-13/6)x + 1/3.