Question

Find the equation of the line. A line that is parallel to the graph of 2x + 3y = 5 and contains the point (3 , -1).​

Answer 1

• 2x+3y=5
• 3y=-2x+5
• y=-2/3x+5/3

On comparison to y=mx+b

• slope=m=-2/3

Parallel lines have equal slopes

• Slope of parallel line=-2/3
• Point (3,-1)

Equation in point slope form

• y-y1=m(x-x1)
• y+1=-2/3(x-3)
• y+1=-2/3x+6
• y=-2/3x+5

Answer 2

Answer:

• $\qquad \boxed{\large \sf \blue{y }\: = \: - \: \frac{2x}{3} \: + \: \red{ 1}}$

$\cal{EXPLANATION:}$

Find the slope of the line that is parallel to 2x + 3y = 5:

• $\boxed{\sf \red{m }\: = \: - \frac{ \green{2}}{ \blue{3}} }$

Substitute and calculate:

• $\large { \{ m \: = - \frac{2}{3} }$
• $\large { \{ m \: = 3 }$
• $\large { \{ y \: = - 1 }$
• $y = mx + b$
• $b \: = \: 1$

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