Mathematics
royalemosley
19

What is the a line that passes through (-2,5) and has a slope of 2/3. Points A(x,3) and B(-2,y) lie on the line

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(1) Answers
Buchinski882

The point-slope form of linear equation is: [latex]y-y_1=m(x-x_1)[/latex] Hence, [latex]\displaystyle y-5= \frac{2}{3}(x+2)\\\\y= \frac{2}{3}x+5 \frac{4}{3} \\\\y=\frac{2}{3}x+6 \frac{1}{3} [/latex] The points A,B are lying on the line, if and only if the next equality is true: [latex]\displaystyle y=\frac{2}{3}x+6 \frac{1}{3} [/latex] Therefore, [latex]\displaystyle A(x,3) \Rightarrow\\\\3=\frac{2}{3}x+6 \frac{1}{3} \\\\9=2x+19\\\\-10=2x\\\\x=-5[/latex] [latex]\displaystyle B(-2,y)\Rightarrow \\\\y=\frac{-4}{3}+6 \frac{1}{3} \\\\y=5[/latex]

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