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)

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kudzordzifrancis kudzordzifrancis · Answer 1 · 2018-11-24T08:28:33+01:00

ANSWER

[tex]y-5=\frac{3}{4}(x-6)[/tex],Yes

[tex]y-5=-\frac{4}{3} (x-2)[/tex],NO

[tex]y-2=-\frac{3}{4} (x-6)[/tex],NO

[tex]y-2=\frac{3}{4}(x-2)[/tex],Yes

EXPLANATION

The line passes through these two points, [tex](6,5)[/tex] and[tex](2,2)[/tex].

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 [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].

We can choose [tex](x_1,y_1)=(6,5)[/tex] and [tex](x_2,y_2)=(2,2)[/tex] or [tex](x_1,y_1)=(2,2)[/tex] and [tex](x_2,y_2)=(6,5)[/tex].

We shall get the same result.

[tex]m=\frac{2-5}{2-6} =\frac{-3}{-4} =\frac{3}{4}[/tex].

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

[tex]y-y_1=m(x-x_1)[/tex].

When we choose [tex](x_1,y_1)=(6,5)[/tex], then we will obtain,

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

When we choose [tex](x_1,y_1)=(2,2)[/tex], then we will obtain,

[tex]y-2=\frac{3}{4}(x-2)[/tex] as the point-slope form.