Question

Passes through the two points (-3,6) and (1,-2). Can someone explain step by step because I don’t understand how to figure this out. (End result should be in slope intercept form[ y=Mx+b])

Answer 1

The equation of the line passing through the points (-3,6) and (1,-2) in slope-intercept form (y=Mx+b) is y = -2x - 4.

Step-by-step explanation:

To find the equation of a line in slope-intercept form, we need to determine both the slope (M) and the y-intercept (b). The slope (M) is given by the formula M = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Given the points (-3,6) and (1,-2), we can calculate the slope as follows:

`\[ M = (-2 - 6)/(1 - (-3)) = (-8)/(4) = -2. \]`

Now that we have the slope, we can use one of the points (let's use (-3,6)) to find the y-intercept (b). The equation for the line in slope-intercept form is y = Mx + b. Plugging in the values, we get:

`\[ 6 = (-2 \cdot -3) + b. \]`

Solving for b:

`\[ 6 = 6 + b \implies b = 0. \]`

Now we have both the slope (M = -2) and the y-intercept (b = 0), so we can write the equation in slope-intercept form:

`\[ y = -2x + 0. \]`

Simplifying further, we get the final answer:

`\[ y = -2x - 4. \]`

Therefore, the equation of the line passing through the points (-3,6) and (1,-2) in slope-intercept form is y = -2x - 4.