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Sagot :
Given
Two points (-8,-3) and (-12,-2)
we are to find the equation of the line
Solution
Steps to find the equation of a line from two points:
1. Find the slope using the slope formula. ...
2. Use the slope and one of the points to solve for the y-intercept (b). ...
3. Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line.
Step 1
[tex]\begin{gathered} \text{Formula for Slope(M)} \\ M=\frac{y_2-y_1}{x_2-x_1_{}} \end{gathered}[/tex][tex]\begin{gathered} x_1=-8_{} \\ x_2=-12 \\ y_1=-3 \\ y_2=-2 \end{gathered}[/tex][tex]\begin{gathered} M=\frac{y_2-y_1}{x_2-x_1} \\ M=\frac{-2-(-3)}{-12-(-8)} \\ \\ \\ M=\frac{-2+3}{-12+8} \\ \\ \\ M=\frac{1}{-4} \end{gathered}[/tex]Step 2
Now, the y-intercept is b
[tex]\begin{gathered} b=y_1-m.x_1 \\ b=\text{ -3 -(}\frac{-1}{4})(-8) \\ b=\text{ -3}-2 \\ b=-5 \end{gathered}[/tex]Step 3
[tex]\begin{gathered} y=mx_{}+b \\ y=-\frac{1}{4}x-5 \end{gathered}[/tex]The final answer
[tex]f(x)=-\frac{1}{4}x-5[/tex]
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