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Write the equation of the line in slope intercept form that passes through the point (-3, 5) and is parallel to y= - 2/3x

2 Answers

7 votes

Answer:


\displaystyle y = -(2)/(3)x + 3

Explanation:

5 = –⅔[–3] + b

2


\displaystyle 3 = b \\ \\ y = -(2)/(3)x + 3

Parallel equations have SIMILAR RATE OF CHANGES [SLOPES], so –⅔ remains as is.

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User Lauw
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13 votes

Answer:

The equation of the line in slope intercept form that passes through the point (-3, 5) and is parallel to y= - 2/3x is
\mathbf{y=-(2)/(3)x+3 }

Explanation:

We need to Write the equation of the line in slope intercept form that passes through the point (-3, 5) and is parallel to y= - 2/3x

The equation in slope-intercept form is:
y=mx+b where m is slope and b is y-intercept.

Finding Slope:

The both equations given are parallel. So, they have same slope.

Slope of given equation y= - 2/3x is m = -2/3

This equation is in slope-intercept form, comparing with general equation
y=mx+b where m is slope , we get the value of m= -2/3

So, slope of required line is: m = -2/3

Finding y-intercept

Using slope m = -2/3 and point (-3,5) we can find y-intercept


y=mx+b\\5=-(2)/(3)(-3)+b\\5=2+b\\ b=5-2\\b=3

So, we get b = 3

Now, the equation of required line:

having slope m = -2/3 and y-intercept b =3


y=mx+b\\y=-(2)/(3)x+3

The equation of the line in slope intercept form that passes through the point (-3, 5) and is parallel to y= - 2/3x is
\mathbf{y=-(2)/(3)x+3 }

User Yothenberg
by
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