Question

Write an equation in point- slope form for the line that passes through the two points given. Use the first point to write the equation. (-8,-6) (4,-3)

Answer 1

To find the point-slope form for the line passing through (-8,-6) and (4,-3), calculate the slope as 1/4 and then use the first point with the slope in the point-slope equation, resulting in y + 6 = 1/4(x + 8).

Step-by-step explanation:

To write the equation of the line in point-slope form that passes through the points (-8,-6) and (4,-3), we must first calculate the slope (m) using the given points. The slope is determined by the formula Δy / Δx or (y2 - y1) / (x2 - x1). Using our points (-8,-6) (x1,y1) and (4,-3) (x2,y2), we calculate the slope as:

m = (-3 - (-6)) / (4 - (-8)) = 3 / 12 = 1 / 4.

Now that we have the slope, we can use the point-slope form of the equation, which is y - y1 = m(x - x1). Using the first point (-8,-6) and the slope 1/4, our equation in point-slope form is:

y - (-6) = 1/4(x - (-8)),

which simplifies to:

y + 6 = 1/4(x + 8).