Question

A line that passes through the point (4,-1) is parallel to the line 3x-2y=9

Answer 1

$\boxed{y+1=\frac{3}{2}(x-4)}$

Explanation:

We can write the equation of the given line in Slope-Intercept form:

$3x-2y=9 \\ \\ \\ Isolating \ y: \\ \\ 3x-9=2y \\ \\ y=\frac{3}{2}x-\frac{9}{2} \\ \\ \\ Where: \\ \\ Slope: \ m=\frac{3}{2} \\ \\ y-intercept: \ b=-\frac{9}{2}$

The line we are looking for is parallel to our given line, that is, they have the same slope. So, writing the Point-Slope form of our unknown line we have:

$y-y_{0}=m(x-x_{0}) \\ \\ m=\frac{3}{2} \\ \\ (x_{0},y_{0})=(4,-1) \\ \\ \\ Substituting \ values: \\ \\ y-(-1)=\frac{3}{2}(x-4) \\ \\ \\ \boxed{y+1=\frac{3}{2}(x-4)}$

Learn more:

Point slope form: brainly.com/question/13771268#

#LearnWithBrainly