Question

What is the equation of the line that passes through (5,-2)and(-3,4)

Answer 1

The equation of the line that passes through (5,-2) and (-3,4) is y = (-3/4)x + 7/4.

Step-by-step explanation:

To find the equation of the line that passes through (5,-2) and (-3,4), we can use the formula for the equation of a straight line, which is y = mx + b.

1. First, calculate the slope (m) using the formula: m = (y2 - y1) / (x2 - x1). In this case, (x1, y1) = (5, -2) and (x2, y2) = (-3, 4). So the slope is m = (4 - (-2)) / (-3 - 5) = 6 / (-8) = -3/4.
2. Next, plug in the values of one of the given points and the slope into the equation. Let's use (5, -2) and the slope m = -3/4: y = (-3/4)x + b. Substitute x = 5 and y = -2.
3. Now solve for b: -2 = (-3/4)(5) + b. Multiply -3/4 and 5: -2 = -15/4 + b. Add 15/4 to both sides: -2 + 15/4 = b. Convert -2 to a fraction with a common denominator: -8/4 + 15/4 = b. Simplify: 7/4 = b.
4. Finally, substitute the value of b back into the equation: y = (-3/4)x + 7/4. This is the equation of the line that passes through (5,-2) and (-3,4).

Answer 2

y = -3/4x + 7/4

Step-by-step explanation:

use the boins to find the slope in the equation y2 - y1/x2 - x1

4 - -2/-3 - 5 = 6/-8 or 3/-4

plug that into the equation: y = mx + b

m = slope b = y-intercept

y = 3/-4x + b now plug in one of the points ex) (5, -2)

(-2) = 3/-4 (5) + b now solve to find the y-intercept: B

b=7/4

now to check your answer plug the other point into the original equation (I have already done this the y-intercept is b=7/4)

here is your final equation y = 3/-4x + 7/4