Respuesta :
Answer:remember that perpendicular lines have slopes that multiply to -1
y-y_1=m(x-x_1) is point-slope form
in point-slope form, it passes through the point (x_1,y_1) and has a slope of m
we want to find the equaiton of the line that is perpendicular to y-3=-4(x+2) and passes through (-5,7)
we need the slope
y-3=-4(x+2)
the slope is -4, but we want perpendicular so
-4 times what=-1?
divide both sides by -4
what=1/4
so the slope of our mystery line is 1/4 and it passe through (-5,7)
so we can write in point slope form as y-7=\frac{1}{4}(x-(-5)) or y-7=\frac{1}{4}(x+5)
the equation is y-7=\frac{1}{4}(x+5)
Step-by-step explanation:
act like it's a fraction you multiply the top number by the bottom number (numerator and the denominator)and then the other but it is keep change flip the same way with the first numbers
The required equation of straight line is 4y = x + 33
What is slope-intercept form ?
One form of the equation of a straight line is called the slope-intercept form because it contains information about these two properties. In the equation y = mx + c the value of m is called the slope, (or gradient), of the line. It can be positive, negative or zero. The value of c is called the y-intercept which means the point of intersection of the graph of straight line with y axis.
What is the concept of parallel and perpendicular line ?
If we have to find a line parallel to a given straight line, then we take the same positive slope value of the given line for finding the required equation.
And if we If we have to find a line perpendicular to a given straight line, then we take the negative reciprocal slope value of the given line for finding the required equation.
Finding the required equation of straight line in slope-intercept form -
Given equation is y - 3 = -4(x + 2)
⇒ y - 3 = -4x -8
⇒ y = -4x - 5
The slope of the given line is -4 when comparing with y = mx + c.
Thus the required slope of straight line is say m1 = -(-1/4) = 1/4
as the required line is perpendicular with the line.
The equation of straight line is y = m1x + c
⇒ y = (x/4) + c
Putting the values of the points (-5,7) in x and y coordinates.
⇒ 7 = (-5/4) + c
⇒ c = 7 + 5/4 = 33/4
Putting value of y-intercept in original equation,
⇒ y = (x/4) + 33/4
∴ 4y = x + 33 which is the required equation.
To learn more about equation of straight line, refer -
https://brainly.com/question/16199524
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