Question

Contains (5,8) and is parallel to the graph of 2x + 3y = 9.

Answer 1

2x+3y=9
3y=9-2x
y=-2/3x+3

Slope is -2/3

8=-2/3(5)+m
Answer: y=-2/3x+34/3

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Answer 2

Answer:

$\displaystyle y = -\frac{2}{3} x + \frac{34}{3} \text{ or } 2x + 3y =34$

Step-by-step explanation:

We want to find the equation of a line that contains the point (5, 8) and is parallel to the graph of:

$\displaystyle 2x + 3y = 9$

Recall that parallel lines have equal slopes.

Find the slope of the given graph by rewriting it in slope-intercept form:

$\displaystyle \begin{aligned} 2x + 3y & = 9 \\ \\ 3y & = -2x + 9 \\ \\ y & = -\frac{2}{3} x + 3 \end{aligned}$

Hence, the slope of the given graph is -2/3. Therefore, the slope of our new line must also be -2/3.

Since we now have a slope and a point, we can consider using the point-slope form:

$\displaystyle y - y_1 = m(x-x_1)$

Substitution yields:

$\displaystyle y - (8) = -\frac{2}{3}(x -( 5))$

We can simplify this into slope-intercept form:

$\displaystyle \begin{aligned} y - 8 & = -\frac{2}{3} x + \frac{10}{3} \\ \\ y & = -\frac{2}{3} x + \frac{34}{3}\end{aligned}$

Or, into standard form:

$\displaystyle \begin{aligned} y & = -\frac{2}{3}x + \frac{34}{3} \\ \\ 3y & = -2x + 34 \\ \\ 2x + 3y & = 34 \end{aligned}$