Question

Write the equation of the line that is parallel to 2x=1-3y and passes through (9,4).

Answer 1

 2x=1-3y 
3y = -2x + 1
y = -2/3x + 1/3
so slope = -2/3

parallel  lines, same slope so slope is also equal -2/3
passes through (9,4)
y = mx + b
b = y - mx
b = 4 - (-2/3)(9)
b = 4 +6
b = 10

equation
y = -2/3(x) + 10

Answer 2

The relationship between parallel lines is that they have the same slope. The equation of the line that is parallel to $2x = 1 - 3y$ and passes through (9,4) is $y=\frac 23x -2$

Given that:

$2x = 1 - 3y$

First, we make y the subject

$2x - 1 = 3y$

Divide both sides by 3

$y = \frac 23x - \frac 13$

A linear equation is represented as:

$y = mx + b$

Where:

$m \to slope$

So, by comparison:

$m = \frac 23$

Parallel lines have the same slope.

So the slope of the line that passes through (9,4) is $m = \frac 23$

The equation is then calculated as:

$y = m(x - x_1) + y_1$

Where:

$m = \frac 23$

$(x_1,y_1) = (9,4)$

So, the equation becomes:

$y = m(x - x_1) + y_1$

$y = \frac 23(x - 9) + 4$

Expand

$y = \frac 23x - 2 \times 3+ 4$

$y=\frac 23x - 6 + 4$

$y=\frac 23x -2$

Hence, the equation of the line that is parallel to $2x = 1 - 3y$ and passes through (9,4) is $y=\frac 23x -2$

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