Question

Find the equation of the line passing through the points (2,11) and (-8,-19).
y = [ ? ]x + [

Answer 1

To find the equation of the line passing through the points (2,11) and (-8,-19), we need to find the slope and the y-intercept of the line. The slope is given by the formula:

m = y2-y1/x2-x1

where (x_1, y_1) and (x_2, y_2) are any two points on the line. Substituting the given points,
{-19 - 11}/{-8 - 2} = {-30}/{-10} = 3

The y-intercept is the value of y when x is zero. To find it, we can use the point-slope form of the equation of a line:

y - y_1 = m(x - x_1)

where m is the slope and (x_1, y_1)is any point on the line. Substituting the slope and one of the given points, we get:

y - 11 = 3(x - 2)

Solving for y, we get:

y = 3x - 6 + 11

y = 3x + 5

Therefore, the equation of the line passing through the points (2,11) and (-8,-19) is:

y = 3x + 5

So, the answer is:

y = [ **3** ]x + [ **5** ]

Answer 2

1. Calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

2. Substitute the values of one of the points and the slope into the equation y = mx + b, and solve for b.

3. Write the final equation of the line using the calculated values of m and b.

Let's calculate the equation of the line passing through the points (2,11) and (-8,-19):

1. Calculate the slope (m):

m = (-19 - 11) / (-8 - 2) = -30 / -10 = 3

2. Choose one of the points, let's use (2,11), and substitute the values into the equation y = mx + b:

11 = 3(2) + b

11 = 6 + b

3. Solve for b:

b = 11 - 6 = 5

4. Write the equation of the line:

y = 3x + 5

Therefore, the equation of the line passing through the points (2,11) and (-8,-19) is y = 3x + 5.

Hope this helps :]