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 [tex]\mathbf{y=-\frac{2}{3}x+3 }[/tex]
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: [tex]y=mx+b[/tex] 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 [tex]y=mx+b[/tex] 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
[tex]y=mx+b\\5=-\frac{2}{3}(-3)+b\\5=2+b\\ b=5-2\\b=3[/tex]
So, we get b = 3
Now, the equation of required line:
having slope m = -2/3 and y-intercept b =3
[tex]y=mx+b\\y=-\frac{2}{3}x+3[/tex]
The equation of the line in slope intercept form that passes through the point (-3, 5) and is parallel to y= - 2/3x is [tex]\mathbf{y=-\frac{2}{3}x+3 }[/tex]
Answer:
[tex]\displaystyle y = -\frac{2}{3}x + 3[/tex]
Step-by-step explanation:
5 = –⅔[–3] + b
2
[tex]\displaystyle 3 = b \\ \\ y = -\frac{2}{3}x + 3[/tex]
Parallel equations have SIMILAR RATE OF CHANGES [SLOPES], so –⅔ remains as is.
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