write the slope intercept form of the equation of the line described
through (-4,-5) perpendicular to y=-2x+5
steps please but not too long though
since the slope of y=-2x+5 is -2, you want a line with slope = 1/2
so start with the point-slope form:
y+5 = 1/2 (x+4)
now just rearrange as desired
perpendicular lines have slopes which are negative-reciprocals
-2 ---> 1/2
using point-slope ... y + 5 = 1/2 (x + 4)
solving for y ... y = 1/2 x - 3
Perpendicular lines have slopes which are negative reciprocals.
In this case:
y = - 2 x + 5
Slope of this line is - 2
Slope of perpendicular line is negative reciprocals :
m = – 1 / ( - 2 ) = 1 / 2
Slope-Intercept form of a straight line :
y = m x + b
y = 1 / 2 x + b
Put x = - 4 , y = - 5 in this equation
- 5 = ( 1 / 2 ) • ( - 4 ) + b
- 5 = - 2 + b
Add 2 to both sides
- 3 = b
b = - 3
So equation of your perpendicular line:
y = 1 / 2 x + b
y = 1 / 2 x - 3
To find the equation of a line in slope-intercept form that is perpendicular to a given line, you need to follow these steps:
Step 1: Determine the slope of the given line.
In the equation y = -2x + 5, the slope is -2. This is because the line is in slope-intercept form (y = mx + b), where the coefficient of x represents the slope.
Step 2: Determine the slope of the perpendicular line.
To find the slope of a line that is perpendicular, take the negative reciprocal of the given line's slope. The negative reciprocal of -2 is 1/2.
Step 3: Use the point-slope form of a line to find the equation.
The point-slope form of a line is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope. We are given the point (-4, -5) and the slope 1/2.
Using the point-slope form and substituting the values, we get:
y - (-5) = 1/2(x - (-4))
Simplifying this equation gives:
y + 5 = 1/2(x + 4)
Rearranging the equation to slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept, we get:
y = 1/2x + 2
Therefore, the slope-intercept form of the equation for the line described, which is perpendicular to y = -2x + 5 and passes through (-4, -5), is y = 1/2x + 2.