Find the equation for the line that passes through the point

Find the equation for the line that passes through the points (-6,9) and (10,6). Give your answer in point-slope form. You do not need to simplify.

Given points (-6,9) and (10,6).

Need to find the equation for the line that passes through the points (-6,9) and (10,6) in point-slope form.

point-slope form of a line is y = mx + c

where m - slope and c is y-intercept.

Slope(m) = Change in y/Change in x

= (6-9)/(10-(-6))

= -3/16

\'c\' can be obtained by substituting m = -3/16 and a point(x,y) = (-6 ,9 ) in y = mx + c

y = mx + c

9 = (-3/16)(-6) + c

9 = 18/16 + c

9 - (18/16) = c

c = (16*9-18)/16

c = 126/16

c = 63/8

Slope-intercept form is y = mx + c

y = (-3/16)x + (63/8)

Therefore, required equation in Slope-intercept form is y = (-3/16)x + (63/8).