Final answer:
To find the equation of a line that passes through two given points, we can use the slope-intercept form of a linear equation: y = mx + b. First, we find the slope using the formula m = (y2 - y1) / (x2 - x1). Then, we substitute one point into the equation to solve for the y-intercept b.
Step-by-step explanation:
To find the equation of a line that passes through two given points, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope of the line and b represents the y-intercept.
First, we need to find the slope (m) of the line using the formula m = (y2 - y1) / (x2 - x1). So, substituting the given coordinates into the formula, we get: m = (1 - 5) / (-2 - 3) = -4 / -5 = 4/5.
Next, we can choose either point to substitute into the slope-intercept form. Let's use (3,5): 5 = (4/5)(3) + b. Solving for b, we have: b = 5 - (4/5)(3) = 5 - 12/5 = 13/5.
Therefore, the equation of the line that passes through the points (3,5) and (-2,1) is y = (4/5)x + 13/5.