a line passes through the points (-4, -4) and (1, 6). write its equation in slope-intercept form. write your…

Explanation:

Step1: Calculate the slope

The slope ( m ) between two points ( (x_1, y_1) ) and ( (x_2, y_2) ) is given by ( m=\frac{y_2 - y_1}{x_2 - x_1} ). Here, ( x_1=-4,y_1 = - 4,x_2 = 1,y_2=6 ). So ( m=\frac{6-(-4)}{1-(-4)}=\frac{6 + 4}{1+4}=\frac{10}{5}=2 ).

Step2: Use point - slope form to find the equation

The point - slope form is ( y - y_1=m(x - x_1) ). Using the point ( (-4,-4) ) and ( m = 2 ), we have ( y-(-4)=2(x-(-4)) ), which simplifies to ( y + 4=2(x + 4) ).

Step3: Convert to slope - intercept form (( y=mx + b ))

Expand the right - hand side: ( y+4=2x+8 ). Subtract 4 from both sides: ( y=2x+8 - 4=2x + 4 ).

Answer:

( y = 2x+4 )