Find the equation of the line through (2,−5),(8,3)(2,−5),(8,3).

Question

Find the equations of the lines through the following pairs of points, in slope intercept form.

Answer 1

Hi Mckenzie! To first solve this question you would need to know the general equation of a line in slope intercept form which is shown by y=mx+b To find the equation of the line we need to know at least 1 point and the slope of the line. In your question, we are given 2 points but we are not given the slope. This means that we need to find the slope of the line first by using the formula for slope which is m=(y2-y1)/(x2-x1) We can set (2,-5) as x1 and y1 respectively and we can set (8,3) as x2 and y2 respectively. Now we can plug in these values into the slope formula m=(y2-y1)/(x2-x1) m=(3-(-5))/(8-2) m=8/6 8/6 can be simplified to 4/3 by diving the numerator and denominator by 2 m=4/3 Now that we found the slope to be 4/3, we plug in the values of x1 and y1 as well as the slope, m, into the point slope form equation of the line which is given by y-y1=m(x-x1) y-y1=m(x-x1) y-(-5)=4/3(x-2) This can be simplified to y+5=4/3(x-2) Then we can distribute the 4/3 which gives us y+5=4/3x - 8/3 Then we isolate the y by subtracting 5 from both sides giving us y=4/3x - 23/3 Your final answer is y=4/3x - 23/3

Answer 2

 

  slope M = (-5-3)/(2-8) = -8/-6 = 4/3

 

  x=8, y=3, M = 4/3

 

y = M x + b

 

3 = (4/3)(8) + b

3 = 32/3 + b

 

9 = 32 + 3b

 

-23 = 3b

 

b = -23/3

 

y = (4/3)X = 23/3