Final answer:
The equation of the line in standard form that passes through the points (2,−10) and (7,−11) is x + 5y = -48 after calculating the slope and eliminating any fractions.
Step-by-step explanation:
To find the equation of the line in standard form that passes through the points (2,−10) and (7,−11), we need to determine the slope and the y-intercept. First, calculate the slope (m) using the slope formula:
m = ∆y / ∆x = (y₂ - y₁) / (x₂ - x₁) = (-11 - (-10)) / (7 - 2) = (-1) / (5) = -1/5
Now that we have the slope, we use one of the points to find the y-intercept. Plugging in the slope and the point (2,−10) into the point-slope form:
y - y₁ = m(x - x₁)
y - (-10) = -1/5(x - 2)
Multiply through by 5 to eliminate the fraction:
5y + 50 = -x + 2
Bring x to the left-hand side and y to the right-hand side to get the standard form:
x + 5y = -48