Question

Given a slope of -2/3 through the point (9,4), what is the:

A) Slope
B) Point-slope form
C) Slope-intercept form
D) Standard form of the equation

Answer 1

The slope is -2/3, the point-slope form is (y - 4) = -2/3(x - 9), the slope-intercept form is y = -2/3x + 10, and the standard form is 2x + 3y = 30.

Step-by-step explanation:

Part A): The slope is -2/3.

Part B): The point-slope form of the equation is given by (y - y1) = m(x - x1), where m is the slope and (x1, y1) is the point through which the line passes.

So, the point-slope form is (y - 4) = -2/3(x - 9).

Part C): To find the slope-intercept form, y = mx + b, we can plug in the slope and the point to solve for b, the y-intercept:

(4) = -2/3(9) + b

4 = -6 + b

b = 10

Therefore, the slope-intercept form is y = -2/3x + 10.

Part D): The standard form of a linear equation is Ax + By = C, where A, B, and C are integers.

To convert the slope-intercept form to standard form, we can multiply each term by 3 to eliminate the fraction:

3y = -2x + 30

Adding 2x to both sides gives:

2x + 3y = 30.