Question

Standard form equation that passes through (-9, 3) and (-6, 1)

Answer 1

The standard form equation of the line that passes through the points (-9, 3) and (-6, 1) is -2x + 3y = 3.

Step-by-step explanation:

The question asks for the standard form equation of a line that passes through the points (-9, 3) and (-6, 1).

To find this, we first calculate the slope (m) of the line using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points.

Substituting the given points, we get m = (1 - 3) / (-6 + 9)

= -2 / 3.

Next, we use point-slope form (y - y1) = m(x - x1) and choose one of the points, for example, (-9, 3),

to get y - 3 = (-2/3)(x + 9).

Expanding and rearranging into standard form (Ax + By = C), we multiply by 3 to clear the fraction: 3(y - 3) = -2(x + 9), which simplifies to -2x + 3y = -6 + 9, resulting in the final standard form equation of -2x + 3y = 3.

Answer 2

The standard form of the equation of a line that passes through (-9, 3) and (-6, 1) is 2x + 3y = -9.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

`y - y_1 = m(x - x_1)`

Where:

• x and y represent the data points.
• m represent the slope.

First of all, we would determine the slope of the downward sloping line by using these points (-9, 3) and (-6, 1);

`Slope(m)=(y_2-y_1)/(x_2-x_1)`

Slope (m) = (1 - 3)/(-6 + 9)

Slope (m) = -2/3

At data point (-9, 3) and a slope of -2/3, an equation for this line can be calculated by using the point-slope form as follows:

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

3y - 9 = -2x - 18

2x + 3y = -18 + 9

2x + 3y = -9