Answer:
[tex]y=\frac{-3}{4}x+\frac{5}{2}[/tex]
Step-by-step explanation:
Our given points: (6, –2) and (–2, 4).
1. Use the slope formula to find the slope
[tex]m=\frac{y_{2} -y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{-2-4}{6-(-2)}[/tex]
[tex]m=\frac{-6}{8}[/tex]
[tex]m=\frac{-3}{4}[/tex]
Therefore, the slope of the line is [tex]\frac{-3}{4}[/tex].
2. Substitute a point and a slope in point-slope form
Point-slope form: [tex]y_{2}-y_{1}=m(x_{2}-x_{1})[/tex]
In point-slope form, the variables [tex]y_{2}[/tex] and [tex]x_{2}[/tex] stay y and x, so when we plug a point into this equation, we plug the x and y variables in [tex]y_{1}[/tex] and [tex]x_{1}[/tex]. We can plug in either given point, (6, –2) and (–2, 4), for this equation to be correct. Below, you can see that I plugged in the first given point.
[tex]y_{2}-y_{1}=m(x_{2}-x_{1})\\y-(-2)=m(x-6)\\y+2=m(x-6)\\y+2=\frac{-3}{4}(x-6)[/tex]
3. Distribute the slope through the parentheses
[tex]y+2=\frac{-3}{4}(x-6)\\y+2=\frac{-3}{4}x-(\frac{-3}{4})(6)\\y+2=\frac{-3}{4}x-\frac{-9}{2}\\y+2=\frac{-3}{2}+\frac{9}{2}[/tex]
4. Solve for the y-variable
This is asking us to isolate the y variable in the equation that we have created in step 3. To isolate the y-variable, all we have to do is move the +2 over to the right side by subtracting both sides by 2.
[tex]y+2=\frac{-3}{4}x+\frac{9}{2}[/tex]
[tex]y=\frac{-3}{4}x+\frac{9}{2}-2[/tex]
[tex]y=\frac{-3}{4}x+\frac{9}{2}-\frac{4}{2}[/tex]
[tex]y=\frac{-3}{4}x+\frac{5}{2}[/tex]
I hope this helps!
