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Sagot :
Answer
[tex]y=-x-4[/tex]where the y-intercept is (0, -4).
Explanation
The equation of the line can be given in the slope-intercept form:
[tex]y=mx+b[/tex]where m is the slope, and b is the y-intercept.
The slope m can be calculated with the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]As we are given two points, (4, -8) and (-7, 3), we can replace the values as follows and simplify:
[tex]m=\frac{3-(-8)}{-7-4}[/tex][tex]m=\frac{3+8}{-7-4}[/tex][tex]m=\frac{11}{-11}=-1[/tex]Thus, our slope is:
[tex]y=(-1)\cdot x+b[/tex][tex]y=-x+b[/tex]Then, we can replace any of the points given in the equation to find the y-intercept. For example, choosing (4, -8):
[tex]-8=-(4)+b[/tex][tex]-8=-(4)+b[/tex]Solving for b :
[tex]-8=-4+b[/tex][tex]-8+4=b[/tex][tex]-4=b[/tex][tex]b=-4[/tex]Finally, our equation is:
[tex]y=-x-4[/tex]
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