Final answer:
To find the equation for the line that passes through two points, we can use the slope-intercept form of a linear equation. By finding the slope and substituting one of the points, we can determine the equation. For the given points (3,4) and (-5,6), the equation is y = -1/4x + 19/4.
Step-by-step explanation:
To find the equation for the line that passes through the points (3,4) and (-5,6), we can use the slope-intercept form of a linear equation: y = mx + b.
First, let's find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1).
Using the coordinates of the two points, we have: m = (6 - 4) / (-5 - 3) = 2 / -8 = -1/4.
Next, we can substitute one of the points and the slope into the equation to find the y-intercept (b). Let's use the point (3,4): 4 = (-1/4)(3) + b. Solving for b, we get: b = 4 + 3/4 = 19/4.
Therefore, the equation for the line is: y = -1/4x + 19/4.