a line passes through the points (-2, -15) and (5, 6). write its equation in slope-intercept form. write…

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,y_1)=(-2,-15) ) and ( (x_2,y_2)=(5,6) ). So, ( m=\frac{6 - (-15)}{5 - (-2)}=\frac{6 + 15}{5 + 2}=\frac{21}{7}=3 ).

Step2: Use point - slope form to find the equation

The point - slope form of a line is ( y - y_1=m(x - x_1) ). Using the point ( (5,6) ) and ( m = 3 ), we have ( y - 6=3(x - 5) ).

Step3: Convert to slope - intercept form

Expand the right - hand side: ( y - 6=3x-15 ). Then, add 6 to both sides: ( y=3x-15 + 6 ), so ( y = 3x-9 ).

Answer:

( y = 3x-9 )