Question

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

Answer 1

Answer:

$\displaystyle y = -\frac{2}{3}x + 3$

Step-by-step explanation:

5 = –⅔[–3] + b

2

$\displaystyle 3 = b \\ \\ y = -\frac{2}{3}x + 3$

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

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Answer 2

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 $\mathbf{y=-\frac{2}{3}x+3 }$

Step-by-step 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

$y=mx+b\\5=-\frac{2}{3}(-3)+b\\5=2+b\\ b=5-2\\b=3$

So, we get b = 3

Now, the equation of required line:

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

$y=mx+b\\y=-\frac{2}{3}x+3$

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