Find an equation of the line that is perpendicular to the line whose equation is 2x – 5y = 3 and passes through (-2, 7). Last time i posted this, the answer was wrong
I answered that correctly
2/25 1:34pm
why do you think it was wrong
Answer choices
1. y = 2.5x + 2
2. y = -2.5x + 2
3. -2x + 7y = -5
4. y = 0.4x + 2
5. y = -0.4x + 2
its not one of the choices
2y + 5x = 4
2y = -5x + 4
y = -2.5x + 2
algebra, right??
To find the equation of a line that is perpendicular to another line, we need to follow a few steps:
1. Determine the slope of the given line.
2. Find the negative reciprocal of the slope to obtain the slope of the perpendicular line.
3. Use the slope of the perpendicular line and the given point to find the equation using the point-slope form.
Let's go through these steps to find the equation of the line perpendicular to the line 2x - 5y = 3 and passing through (-2, 7):
Step 1: Determine the slope of the given line.
The given equation 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.
For the equation 2x - 5y = 3, we can rewrite it in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Rearranging the equation, we get:
-5y = -2x + 3
Dividing by -5, we have:
y = (2/5)x - 3/5
Thus, the slope of the given line is 2/5.
Step 2: Find the negative reciprocal of the slope.
To find the slope of the perpendicular line, we need to find the negative reciprocal of the slope of the given line.
The negative reciprocal of 2/5 is -5/2.
Step 3: Use the slope of the perpendicular line and the given point to find the equation using the point-slope form.
Using the point-slope form (y - y1 = m(x - x1)), where (x1, y1) is the given point and m is the slope, we can substitute the values (-2, 7) and -5/2 into the equation:
y - 7 = (-5/2)(x - (-2))
Simplifying further:
y - 7 = (-5/2)(x + 2)
To convert this equation to a standard form (Ax + By = C), we can multiply through by 2 to eliminate the fraction:
2(y - 7) = -5(x + 2)
2y - 14 = -5x - 10
5x + 2y = -4
Therefore, the equation of the line that is perpendicular to 2x - 5y = 3 and passes through (-2, 7) is 5x + 2y = -4.