Question

Write an equation in slope intercept form that passes through -2, 3 and Is parallel to the line with equation 3X +2y=6

Answer 1

The equation of line is:  $y=-\frac{3}{2}x$ as the y-intercept is zero

Step-by-step explanation:

Given

(-2,3)

Equation of line => 3x+2y=6

Converting the equation in slope intercept form

$3x+2y=6\\2y=-3x+6\\Dividing\ both\ sides\ by\ 2\\\frac{2y}{2}=-\frac{3}{2}x+\frac{6}{2}\\y=-\frac{3}{2}x+3$

The co-efiicient of x is the slope of the fiven line

So,

m=-3/2

The line parallel to given line will have the same slope as slopes of two parallel lines are equal

Now,

Slope-intercept form is:

$y=mx+b$

Putting the value of slope

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

to find the value of b, put (-2,3) in the equation

$3=-\frac{3}{2}(-2)+b\\3=3+b\\b=0$

Putting the value of b and m

$y=-\frac{3}{2}x+0\\y=-\frac{3}{2}x$

Hence,

The equation of line is:  $y=-\frac{3}{2}x$ as the y-intercept is zero

Keywords: Slope-intercept form, Slope

Learn more about slope-intercept form at:

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