Question

Write the equation of the line that passes through the points (9, -2) and (4, 2). Put

your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.

Answer 1

The line equation in point-slope form that passes through the points (9, -2) and (4, 2) is y = (-4/5)x + 26/5 after calculating the slope and applying the point-slope equation using one of the given points.

Step-by-step explanation:

To find the equation of the line that passes through the points (9, -2) and (4, 2), we first need to calculate the slope of the line (m) using the formula m = (y₂ - y₁) / (x₂ - x₁).

Plugging the points into the formula gives us m = (2 - (-2)) / (4 - 9) = 4 / (-5) = -4/5.

Now, using one of the points and the slope, we can put the equation in the point-slope form, which is y - y₁ = m(x - x₁).

Using the point (9, -2), we get y - (-2) = (-4/5)(x - 9), which simplifies to y + 2 = (-4/5)x + (36/5).

To reduce to fully reduced point-slope form, we would subtract 2 from both sides, ending with y = (-4/5)x + (36/5 - 10/5) or y = (-4/5)x + 26/5.

So, the equation of the line passing from the points (9, -2) and (4, 2) is y = (-4/5)x + 26/5.