Find the equation of a line that is perpendicular to the line y = x + 7 and has the same y-intercept as 3y = 2x - 9. state the answer in standard form.

The standard for is x + y = -3

Step-by-step explanation:

To start, we know that the slope of perpendicular lines are opposite and reciprocal. Since the perpendicular line has a slope of 1, we know the new line will have a slope of -1.

To find the intercept of the second equation, solve for y and look for the constant.

3y = 2x - 9

y = 2/3x - 3

This gives us an intercept of -3.

Now that we have the slope and intercept we can use slope-intercept form and plug in the information. Then we simply need to solve for the constant.

y = mx + b

y = -x - 3

x + y = -3

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form