Question

При каком значении а прямая ах+2у=11 проходит через точку С (7;5)?

Answer 1

C(7;5)
$x_C=7;y_C=5$
$a*7+2*5=11$
$7a+10=11$
$7a=11-10$
$7a=1$
$a=\frac{1}{7}$

Answer 2

Finding the Equation of a Line Passing Through a Given Point

To find the equation of a line passing through a given point, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is the given point, and m is the slope of the line.

Given Information

The given point is C(7, 5).

Calculating the Slope

The equation 2y = 11 can be rewritten as y = 11/2. This represents a horizontal line, and its slope is 0.

Equation of the Line

Using the point-slope form, the equation of the line passing through point C(7, 5) with a slope of 0 is: y - 5 = 0(x - 7)

Simplifying this, we get: y - 5 = 0 which further simplifies to: y = 5

Therefore, the equation of the line passing through the point C(7, 5) is y = 5.