Write the equation of the line that satisfies the given conditions. Express the final equation in standard form.
Contains the point (-8, 5) and is perpendicular to the line 2x − y = 4
2x − y = 4 has a slope of 2
so your new line must have a slope of -1/2
new equation:
y - 5 = (-1/2)(x + 8)
clean it up to whatever version you need
To find the equation of a line that is perpendicular to the given line, we need to determine the slope of the given line first. The equation of the given line is in the form Ax + By = C, where A is the coefficient of x, B is the coefficient of y, and C is the constant term.
In this case, the given line equation is 2x − y = 4. To find the slope of this line, let's rearrange the equation into slope-intercept form (y = mx + b):
2x − y = 4
- y = -2x + 4
y = 2x - 4
The slope of the given line is 2 (the coefficient of x in the slope-intercept form). Since we want to find a line perpendicular to this, we need to find the negative reciprocal of 2.
The negative reciprocal of 2 is -1/2. This will be the slope of the perpendicular line.
Next, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where (x1, y1) represents the given point on the line. In this case, the point is (-8, 5), so x1 = -8 and y1 = 5.
Substituting the values into the point-slope form,
y - 5 = (-1/2)(x - (-8))
Simplifying,
y - 5 = (-1/2)(x + 8)
Expanding,
y - 5 = (-1/2)x - 4
Rearranging it in standard form (Ax + By = C),
(1/2)x + y = -9
Therefore, the equation of the line that satisfies the given conditions is (1/2)x + y = -9 in standard form.