Final answer:
To find the equation for the line passing through two points, we calculate the slope and use the point-slope form of the equation.
Step-by-step explanation:
To find the equation for the line that passes through the points (5,4) and (3,7), we can first calculate the slope using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates of the points, we get:
m = (7 - 4) / (3 - 5) = -3 / -2 = 1.5
Next, we can use the point-slope form of the equation:
y - y1 = m(x - x1)
Substituting one of the points and the slope, we have:
y - 4 = 1.5(x - 5)
Simplifying, we get:
y = 1.5x - 6.5