Question

Identify the equation that describes the line in slope-intercept form.

slope =−1/3, point (−2,3) is on the line

Answers are attached. Please help

Answer 1

The equation of the line with slope −1/3 and passing through the point (−2,3) is y = −1/3x + 7/3.

Step-by-step explanation:

To identify the equation of the line in slope-intercept form given a slope of −1/3 and a point (−2,3) on the line, we start by using the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. In this case, m = −1/3.

We can then use the given point to solve for b. Plugging in the point values into the equation gives us 3 = (−1/3)(−2) + b. Solving for b gives us 3 = 2/3 + b, which simplifies to b = 7/3. Therefore, the equation of the line is y = −1/3x + 7/3.

Answer 2

The equation that describes the line in slope-intercept form with a slope of -1/3 and the point (-2, 3) on the line is y = -1/3x + 7/3.

Step-by-step explanation:

The equation that describes the line in slope-intercept form with a slope of -1/3 and the point (-2, 3) on the line can be found using the formula: y = mx + b, where m is the slope and b is the y-intercept.

First, substitute the given slope (-1/3) for m and the coordinates of the point (-2, 3) for x and y:

3 = (-1/3)(-2) + b

Simplify the equation:

3 = 2/3 + b

Next, solve for b by subtracting 2/3 from both sides of the equation:

3 - 2/3 = b

Convert 3 to a fraction with the same denominator as 2/3:

9/3 - 2/3 = b

Combine like terms:

7/3 = b

So, the equation that describes the line in slope-intercept form is y = -1/3x + 7/3.