Question

А)прямая y=3x+l проходит чепез точку А(17;30) найдите l и определите, проходит ли эта прямая через точку В(25;54) б)прямая у= -2,5х+ l походит через точку М(-20;66) найдите l и определите, проходит ли эта прямая через точку С(20;36) помогите пожайлуста

Answer 1

1) найдем коэффициент
30=3×17+l
l=-21
уравнение прямой y=3x-21
3×25-21=75-21=54
точка В (25;54) лежит на прямой
2) найдем коэффициент
66=-2,5×(-20)+l
l=16
уравнение прямой y=-2,5x+16
-2,5×20+16=-34 <>36
точка С (20;36) не лежит на прямой

Answer 2

Task A: Finding the equation of a line passing through point A(17, 30) and determining if it passes through point B(25, 54)

To find the equation of a line passing through point A(17, 30), we need to determine the slope (l) of the line. The slope (l) can be found using the formula:

l = (y2 - y1) / (x2 - x1)

where (x1, y1) = (17, 30) and (x2, y2) = (25, 54).

Substituting the values into the formula, we get:

l = (54 - 30) / (25 - 17) = 24 / 8 = 3

So, the slope (l) of the line passing through point A(17, 30) is 3.

Now, 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.

Substituting the values of the slope (m = 3) and the coordinates of point A (x = 17, y = 30) into the equation, we can solve for b:

30 = 3 * 17 + b

Simplifying the equation, we get:

30 = 51 + b

Subtracting 51 from both sides, we find:

b = -21

Therefore, the equation of the line passing through point A(17, 30) is:

y = 3x - 21.

To determine if this line passes through point B(25, 54), we can substitute the coordinates of point B into the equation and check if the equation holds true:

54 = 3 * 25 - 21

Simplifying the equation, we get:

54 = 75 - 21

54 = 54

Since the equation holds true, we can conclude that the line y = 3x - 21 passes through point B(25, 54).

Task B: Finding the equation of a line passing through point M(-20, 66) and determining if it passes through point C(20, 36)

To find the equation of a line passing through point M(-20, 66), we need to determine the slope (l) of the line. Using the same formula as before:

l = (y2 - y1) / (x2 - x1)

where (x1, y1) = (-20, 66) and (x2, y2) = (20, 36).

Substituting the values into the formula, we get:

l = (36 - 66) / (20 - (-20)) = -30 / 40 = -0.75

So, the slope (l) of the line passing through point M(-20, 66) is -0.75.

Using the slope-intercept form of a linear equation, we can write the equation as:

y = mx + b

Substituting the values of the slope (m = -0.75) and the coordinates of point M (x = -20, y = 66) into the equation, we can solve for b:

66 = -0.75 * (-20) + b

Simplifying the equation, we get:

66 = 15 + b

Subtracting 15 from both sides, we find:

b = 51

Therefore, the equation of the line passing through point M(-20, 66) is:

y = -0.75x + 51.

To determine if this line passes through point C(20, 36), we can substitute the coordinates of point C into the equation and check if the equation holds true:

36 = -0.75 * 20 + 51

Simplifying the equation, we get:

36 = -15 + 51

36 = 36

Since the equation holds true, we can conclude that the line y = -0.75x + 51 passes through point C(20, 36).

I hope this helps! Let me know if you have any further questions.