Question

Use slope-intercept form, y = mx + b to find the equation of the line that passes through the points (−6, 1) and (3, 4).
A. y = –3x + 5
B. y = 3x – 5
C. y=1/3x+3
D. y=-1/3x+5

Answer 1

Answer:

y=mx+b

as m=y2-y1/x2-x1

y=(y2-y1/x2-x1)x+b

y=(4-1/3-(-6))x+b

and b=4+1=5

y=3/9 x +5

y=1/3x+5

Answer 2

Option C is the answer

Step-by-step explanation:

since there are two points (-6, 1) and (3,4) we find the slope using these two points.

i.e., $m = \frac{y_{2} - y_{1}  }{x_{2} - x_{1} }$

      $m = \frac{4 - 1}  {3 + 6}\\ m = \frac{3}{9}\\ m= \frac{1}{3}$

By using the slope - intercept form, the equation of the line is ,

$y = mx + c\\y = \frac{1}{3}x + c$

Since 'c' is the y-intercept, the value of 'c' is 4 - 1 = 3

∴ c = 5

put the 'c' value in the above equation of slope intercept form, then we get

$y = \frac{1}{3} x + 3$

Hence the answer is option C.