Answer:
[tex]y=-\frac{3}{2}x+\frac{7}{2}[/tex]
Step-by-step explanation:
So when two lines are parallel there slopes are the same, but there y-intercepts are different, since if they had the same y-intercept, then they would be the same exact line. To convert an equation into slope-intercept form you simple isolate y by moving everything else to the other side, and then divide by the coefficient of y so the coefficient of y becomes 1. This will give you the equation in the form: y=mx+b where m is the slope and b is the y-intercept (because when the linear equation crosses the y-axis, the x is 0, thus mx will be 0, leaving only b, so the y-intercept is b).
Original Equation:
3x + 2y = 4
Subtract 3x from both sides
2y = -3x + 4
Divide both sides by 2
y = -3/2x + 2
Generally any parallel line will be in the form:
[tex]y=-\frac{3}{2}x + b\ \ \ \ \ b\ne2[/tex]. Since as stated before if two lines have the same slope and y-intercept, they're the same line, which is not the same as parallel, since parallel lines never intersect.
So since we're given a point in the parallel line (-1, 5) we can plug those values into the equation to find the value of b
[tex]5=-\frac{3}{2}(-1) + b[/tex]
Multiply and
[tex]5=\frac{3}{2}+ b[/tex]
Convert 5 into a fraction with a denominator of 2
[tex]\frac{5}{1} * \frac{2}{2} = \frac{10}{2}[/tex]
Write equation using this form of 5:
[tex]\frac{10}{2}=\frac{3}{2}+b[/tex]
Subtract 3/2 from both sides
[tex]\frac{7}{2}=b[/tex]
Now take this value and input it into the slope-intercept form to finish the equation: [tex]y=-\frac{3}{2}x+\frac{7}{2}[/tex]
