Question

What is an equation of the line that passes through the points (4,-5) and (-2,7)

Answer 1

y=-2x+3

Explanation:

To find the equation of the line passing through the points (4, -5) and (-2, 7), we can use the point-slope form of the equation of a line:

y - y₁ = m(x - x₁)

where (x₁, y₁) represents one of the given points, and m is the slope of the line.

Let's calculate the slope (m) using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Substituting the coordinates of the points (4, -5) and (-2, 7) into the formula:

m = (7 - (-5)) / (-2 - 4)

m = 12 / -6

m = -2

Now we have the slope (m = -2), and we can choose one of the given points (4, -5) to substitute into the point-slope form. Let's use (4, -5):

y - (-5) = -2(x - 4)

Simplifying:

y + 5 = -2(x - 4)

y + 5 = -2x + 8

y = -2x + 3

Answer 2

y = -2x + 3

Explanation:

y2 - y1/ x2 - x1

7 - (-5) / -2 - 4

-2

The slope is -2.

To find the y-intercept, you need to plug the coordinates into the equation.

y = -2x + b

7 = -2(-2) + b

7 = 4 + b

3 = b

y = -2x + 3