Question

A line passes through the points (6,5) and (2,2) . Select Yes or No to tell whether each equation describes this line. Equation Yes No y−5=34(x−6) y−5=−43(x−2) y−2=−34(x−6) ​y−2=34(x−2)​

Answer 1

ANSWER

$y-5=\frac{3}{4}(x-6)$,Yes

$y-5=-\frac{4}{3} (x-2)$,NO

$y-2=-\frac{3}{4} (x-6)$,NO

$y-2=\frac{3}{4}(x-2)$,Yes

EXPLANATION

The line passes through these two points, $(6,5)$ and$(2,2)$.

We can use these two points to determine the slope of the line.

The formula for finding the slope of a line when at least two points are known is $m=\frac{y_2-y_1}{x_2-x_1}$.

We can choose $(x_1,y_1)=(6,5)$ and $(x_2,y_2)=(2,2)$ or $(x_1,y_1)=(2,2)$ and $(x_2,y_2)=(6,5)$.

We shall get the same result.

$m=\frac{2-5}{2-6} =\frac{-3}{-4} =\frac{3}{4}$.

We now determine the equation of the line using the poit-slope formula,

$y-y_1=m(x-x_1)$.

When we choose $(x_1,y_1)=(6,5)$, then we will obtain,

$y-5=\frac{3}{4}(x-6)$ as the point-slope form.

When we choose $(x_1,y_1)=(2,2)$, then we will obtain,

$y-2=\frac{3}{4}(x-2)$ as the point-slope form.