- Convert linear equations to slope-intercept form
Slope–intercept form is [latex]y=mx+b[/latex]. Find this form by solving for [latex]y[/latex].
Convert each to [latex]y=mx+b[/latex].
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[latex]3x+2y=8[/latex]
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[latex]y-5=\tfrac{4}{3}(x+6)[/latex]
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[latex]2(y+1)=5(x-2)-3[/latex]
- [latex]4x-3y=12[/latex]
[latex]\begin{align} 4x-3y &= 12 \\ -3y &= -4x+12 && \text{subtract }4x \\ y &= \frac{4}{3}x-4 && \text{divide by }-3 \end{align}[/latex]
- [latex]y+2=-2(x-3)[/latex]
[latex]\begin{align} y+2 &= -2(x-3) \\ y+2 &= -2x+6 && \text{distribute }-2 \\ y &= -2x+4 && \text{subtract }2 \end{align}[/latex]
- [latex]2(y+1)=5(x-2)-3[/latex]
[latex]\begin{align} 2(y+1) &= 5(x-2)-3 \\ 2y+2 &= 5x-10-3 && \text{distribute} \\ 2y &= 5x-15 && \text{subtract }2 \\ y &= \frac{5}{2}x-\frac{15}{2} && \text{divide by }2 \end{align}[/latex]