Final answer:
To find the equation of a line parallel to another line, use the same slope as the given line. The equation of the line parallel to 2x + 3y = 10 and passing through (-5, -2) is y = -2/3x - 16/3.
Step-by-step explanation:
To find the equation of a line parallel to another line, we need to use the same slope as the given line. The given line has the equation 2x + 3y = 10. To find the slope of this line, we need to rearrange the equation into slope-intercept form y = mx + b. So, subtracting 2x from both sides gives us 3y = -2x + 10. Dividing both sides by 3, we get y = (-2/3)x + 10/3. The slope of this line is -2/3. Since the line we need to find is parallel to this line, it will have the same slope of -2/3.
Now, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1). Using the point (-5, -2) and the slope -2/3, we have y - (-2) = -2/3(x - (-5)). Simplifying this equation gives us y + 2 = -2/3(x + 5). Rearranging into slope-intercept form, we get y = -2/3x - 16/3. So, the equation of the line parallel to 2x + 3y = 10 and passing through (-5, -2) is y = -2/3x - 16/3.
Learn more about Equation of slope-intercept form