Question

indicate in standard form the equation of the line passing through the given pointsE(-2,2),P(5,1)enter your answer in the blank question box

Answer 1

Answer:

x+7y=12

Explanation:

The standard form of the equation of a line is: ax+by=c

To determine the equation of the line passing through E(-2,2) and P(5,1).

First, we determine the slope.

$\begin{gathered} \text{Slope}=\frac{Change\text{ in y}}{Change\text{ in x}} \\ =\frac{1-2}{5-(-2)} \\ =\frac{-1}{7} \\ m=-\frac{1}{7} \end{gathered}$

Next, we determine the y-intercept.

Using the point (5,1)

When x=5, y=1

$\begin{gathered} y=mx+b \\ 1=-\frac{1}{7}(5)+b \\ b=1+\frac{5}{7} \\ b=\frac{12}{7} \end{gathered}$

Therefore, the equation of the line is:

$\begin{gathered} y=-\frac{1}{7}x+\frac{12}{7} \\ y=\frac{-x+12}{7} \\ 7y=-x+12 \\ \text{Expressing in standard form, we have:} \\ x+7y=12 \end{gathered}$