Respuesta :
Given:
a.) Parallel to a line: 2x + 3y = - 15
b.) Passes through the point (3, 4)
Let's find the equation of a line parallel to 2x + 3y = -15.
Note: Since the line that we are looking at is parallel to 2x + 3y = -15, they should have the same slope.
Step 1: Let's determine the slope of the line based on its slope-intercept form: y = mx + b.
[tex]\begin{gathered} \text{ 2x + 3y = -15} \\ \text{ 3y = -15 - 2x} \\ \text{ }\frac{\text{3y}}{\text{ 3}}\text{ = }\frac{\text{-2x - 15}}{3} \\ \text{ y = -}\frac{2}{\text{ 3}}x\text{ - 15} \end{gathered}[/tex]Therefore, the slope of the line (m) is -2/3.
Step 2: Using the slope = -2/3 and x,y = 3,4. Plug it in y = mx + b to find the y-intercept of the parallel line.
[tex]\begin{gathered} \text{ y = mx + b} \\ \text{ 4 = (-}\frac{2}{3})(3)\text{ + b} \\ \text{ 4 = -2 + b} \\ \text{ b = 4 + 2} \\ \text{ b = 6} \end{gathered}[/tex]Step 3: Let's now complete the equation. Substitute the slope (m) = -2/3 and b = 6 in y = mx + b.
[tex]\begin{gathered} \text{ y = mx + b} \\ \text{ y = (-}\frac{2}{3})x\text{ + (6)} \\ \text{ y = -}\frac{2}{3}x\text{ + 6} \end{gathered}[/tex]Therefore, the equation of the line parallel to 2x + 3y = -15 is:
[tex]\text{ y = -}\frac{2}{3}x\text{ + 6}[/tex]