3 The line through (2, -4) and (x, 1) has a slope of -5. Determine the equation of the
line and the value of x.
Ответы
To determine the equation of the line through the points (2, -4) and (x, 1) with a slope of -5, you can use the point-slope form of the equation of a line:
y - y_1 = m(x - x_1)
where (x1, y1) is a point on the line, m is the slope, and (x, y) are the coordinates of any other point on the line.
In this case, you have the point (2, -4) and the slope m = -5:
y - (-4) = -5(x - 2)
Now, simplify the equation:
y + 4 = -5(x - 2)
Next, distribute the -5 on the right side:
y + 4 = -5x + 10
Now, isolate y by subtracting 4 from both sides:
y = -5x + 6
So, the equation of the line is y = -5x + 6.
To find the value of x, you can use the fact that the line passes through the point (x, 1). Substitute this point into the equation:
1 = -5x + 6
Now, solve for x:
5x = 6 - 1
5x = 5
x = 1
So, the value of x is 1.
лінія і значення x.