Question

Which is the equation in slope-intercept form for the line that passes through (−1, 5) and is parallel to 3x + 2y = 4?

Answer 1

Answer:

$y=-\frac{3}{2}x+\frac{7}{2}$

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:

$y=-\frac{3}{2}x + b\ \ \ \ \ b\ne2$. 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

$5=-\frac{3}{2}(-1) + b$

Multiply and

$5=\frac{3}{2}+ b$

Convert 5 into a fraction with a denominator of 2

$\frac{5}{1} * \frac{2}{2} = \frac{10}{2}$

Write equation using this form of 5:

$\frac{10}{2}=\frac{3}{2}+b$

Subtract 3/2 from both sides

$\frac{7}{2}=b$

Now take this value and input it into the slope-intercept form to finish the equation: $y=-\frac{3}{2}x+\frac{7}{2}$