Question

Find the equation, in slope-intercept form, of the line through the pair of points

Answer 1

Answer:

$y=-\frac{3}{2}x+\frac{7}{2}$

Step-by-step explanation:

We do not have enough information for slope intercept form. But we can use the point-slope formula to find the information. The formula is $y -y_{1} =m(x -x_{1})$ where we substitute a point (x,y) for $(x_{1},y_{1})$.  

We do not have m for the slope. But we do have (1,-2) and (-3, 4). We input the points for $x_{1} =1\\y_{1}=-2$ and $x=-3\\y=4$.  

$(4-(-2))=m (-3-1)$

We now simplify the parenthesis and solve for m.

$(4+2)=m (-3+-1)\\6=m(-4)=$

We divide by -4 on both sides and find $m=-\frac{6}{4} =-\frac{3}{2}$. We substitute m into the point slope form with one coordinate pair.

$y-(-2)=-\frac{3}{2}(x-1)\\y+2=-\frac{3}{2}(x-1)\\y+2=-\frac{3}{2}x+\frac{3}{2}\\y+2-2=-\frac{3}{2}x+\frac{3}{2}-2\\y=-\frac{3}{2}x+\frac{3}{2}+\frac{4}{2} \\y=-\frac{3}{2}x+\frac{7}{2}$

After simplifying the parenthesis, we subtracted 2 from both sides. We converted 2 into a fraction with 2 as the denominator.

This is slope intercept form$y=-\frac{3}{2}x+\frac{7}{2}$. The line has slope -3/2 and y-intercept (0,7/2) or b=7/2.