Nicky156
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HELP PLEASE!


1. The equation of line m is 4x+5y=−2.

What is the slope of a line that is perpendicular to line m?


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2. What is the equation of a line that is parallel to −x+3y=6 and passes through the point (3, 5) ?


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Respuesta :

Unicrumb

1.) The slope equals -5/4 because if we change the 4x+5y=-2 to a slope-intercept form then we can easily see the m (slope) and from that you switch the sign of the number and switch the numbers (ex. -1/2 = 2, 3 = -1/3). To get to the slope-intercept, you subtract 4x from both sides to get 5y=4x-2, then divide both sides by the 5 next to y to get y=4/5x-2/5.

2.) The equation would be y=1/3x+5 because if make the equation into a slope-intercept form by adding the x to both sides to get 3y=x+6 then divide both sides by 3 for y=1/3+2, then we can see the slope is 1/3 and since parallel lines have the same slope, you know the new line's slope is 1/3. Now if we put the slope into a new equation you'll get y=1/3x+b, so you then substitute the point's x and y in the equation for 5=1/3(3)+b, and then solve for b which is 5. Putting the y-intercept (b) and the slope into an equation, you get y=1/3x+5.

abidemiokin

The slope of a line that is perpendicular to line m is 5/4

When two lines are perpendicular to each other, the product of their slope is -1

The equation of a line that is parallel to −x+3y=6 and passes through the point (3, 5) is 3y - x = 12

Let the slopes of the lien be a and b, if the slope of the lines are perpendicular, hence ab = -1

Given the equation 4x+5y=−2.

Rewrite in standard form

5y = -4x - 2

y = -4/5 x - 2/5

Slope if the line a = -4/5

We are to get the slope of the line perpendicular.

Recall that ab = -1

-4/5 b = -1

-4b = -5

b = 5/4

Hence the slope of a line that is perpendicular to line m is 5/4

2) The standard equation of a line in point slope form us y-y0 = m(x-x0)

Given the equation -x + 3y = 6

3y = x + 6

y = 1/3 x + 2

Slope  = 1/3

Point = (3, 5)

Get the required equation:

y - 5 = 1/3(x - 3)

3(y - 5) = x - 3

3y - 15  = x - 3

3y - x = 12

Hence the equation of a line that is parallel to −x+3y=6 and passes through the point (3, 5) is 3y - x = 12

Learn more here: https://brainly.com/question/13140886

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