Answer:
y=1/4 x +11
Step-by-step explanation:
So this is a word problem but it isn't too bad to figure what they want: They are looking for a line that is perpendicular to y=-4x-6 and goes through (-4,10).
So we are looking for an equation whose slope is the opposite reciprocal of the given equation's slope.
The given equation has a slope of -4
The opposite reciprocal of -4 is 1/4 so that is the slope of our new line.
So we know our equation is in the form of y=1/4 x+b
Now we are given that this line should go through (-4,10) so plug it in to find b.
10=1/4 * (-4)+b
10=-1+b
11=b
So the equation is y=1/4 x+11
Answer: [tex]y=\frac{1}{4}x+11[/tex]
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
Given the equation of the line [tex]y= -4x - 6[/tex], you can identify that the slope is:
[tex]m=-4[/tex]
By definition, the slopes of perpendicular lines are negative reciprocals, then the slope of equation of the line that represents the new path which will be built perpendicular to other path, is:
[tex]m=\frac{1}{4}[/tex]
Knowing that the path will intersect at the point (-4 ,10), you need to substitute the slope and this point into [tex]y=mx+b[/tex] and solve for "b":
[tex]10=\frac{1}{4}(-4)+b\\\\10+1=b\\\\b=11[/tex]
Therefore, the equation that represents the new path is:
[tex]y=\frac{1}{4}x+11[/tex]
