Write an equation in slope-intercept form of the line through points S(-7,-6) and T(10,8).
slope: 14/17
y-8 = 14/17 (x-10)
y = 14/17 x - 4/17
To find the equation of the line through two given points in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b).
Step 1: Calculate the slope (m)
The slope (m) is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Given the points S(-7, -6) and T(10, 8), we can substitute the coordinates into the formula:
m = (8 - (-6)) / (10 - (-7))
m = 14 / 17
Step 2: Determine the y-intercept (b)
To find the y-intercept (b), we can substitute the slope (m) and one of the given points (e.g., T) into the slope-intercept form equation (y = mx + b) and solve for b:
8 = (14/17)(10) + b
8 = (140/17) + b
b = 8 - (140/17)
b = (136/17)
Step 3: Write the equation
Now that we have the slope (m) and y-intercept (b), we can write the equation of the line in slope-intercept form:
y = (14/17)x + (136/17)
Therefore, the equation of the line through points S(-7, -6) and T(10, 8) is y = (14/17)x + (136/17).