Write the slope-intercept form of the equation that passes through the given points. (separate equations for each of them)1. (10,-3) (5,-2)2. (6,2) (7,5)3. (4,4) (-7,4)

Answer:Part 1) [tex]y=-\frac{1}{5}x-1[/tex]Part 2) [tex]y=3x-16[/tex]Part 3) [tex]y=4[/tex]Step-by-step explanation:we know thatThe equation of the line into slope intercept form is equal to[tex]y=mx+b[/tex]wherem is the slope b is the y-interceptPart 1) we have(10,-3) (5,-2)Find the slopeThe formula to calculate the slope between two points is equal to [tex]m=\frac{y2-y1}{x2-x1}[/tex] substitute[tex]m=\frac{-2+3}{5-10}[/tex] [tex]m=\frac{1}{-5}[/tex] [tex]m=-\frac{1}{5}[/tex] Find the value of bwe have [tex]m=-\frac{1}{5}[/tex] [tex]point (10,-3)[/tex]substitute in the equation [tex]y=mx+b[/tex]  and solve for b[tex]-3=-\frac{1}{5}(10)+b[/tex][tex]-3=-2+b[/tex][tex]b=-3+2=-1[/tex]substitute[tex]y=-\frac{1}{5}x-1[/tex]Part 2) we have(6,2) (7,5)Find the slopeThe formula to calculate the slope between two points is equal to [tex]m=\frac{y2-y1}{x2-x1}[/tex] substitute[tex]m=\frac{5-2}{7-6}[/tex] [tex]m=\frac{3}{1}[/tex] [tex]m=3[/tex] Find the value of bwe have [tex]m=3[/tex] [tex]point (6,2)[/tex]substitute in the equation [tex]y=mx+b[/tex]  and solve for b[tex]2=3(6)+b[/tex][tex]2=18+b[/tex][tex]b=2-18=-16[/tex]substitute[tex]y=3x-16[/tex]Part 3) we have(4,4) (-7,4)Find the slopeThe formula to calculate the slope between two points is equal to [tex]m=\frac{y2-y1}{x2-x1}[/tex] substitute[tex]m=\frac{4-4}{-7-4}[/tex] [tex]m=\frac{0}{-11}[/tex] [tex]m=0[/tex] This is a horizontal line (parallel to the x-axis)The y-intercept b is equal to the y-coordinatethereforeThe equation of the line is [tex]y=4[/tex]