Write an equation of the line that passes through (3,4) and is perpendicular to the line defined by x- 2y = 5. Write the answer in slope-intercept form (if
possible) and in standard form (Ax+ By = C) with smallest integer coefficients. Use the "Cannot be written" button, if applicable.
First, let's find the slope of the given line x - 2y = 5.
x - 2y = 5
-2y = -x + 5
y = 1/2x - 5/2
The slope of the given line is 1/2.
Since the line we want to find is perpendicular to the given line, its slope will be the negative reciprocal of 1/2, which is -2.
Now we have the slope (-2) and the point (3,4). We can use the point-slope form to find the equation of the line:
y - y₁ = m(x - x₁)
y - 4 = -2(x - 3)
y - 4 = -2x + 6
y = -2x + 10
So, the equation of the line passing through (3,4) and perpendicular to x - 2y = 5 is y = -2x + 10 in slope-intercept form.
Converting this to standard form:
2x + y = 10
Therefore, the equation of the line in standard form is 2x + y = 10.