Question

write and equation of a line in a slope-intercept form (y=mx+b) that contains the point (2,3) and is parallel to a line that contains the points (-3,8) and (-1,4)

Answer 1

if the line is paralel to the line that contains the points (-3,8) and (-1,4), it will have the same slope

so we can calculate the slope using this two points:

m = (y2 - y1)/(x2 - x1) = (4-8)/(-1 -(-3)) = (4 - 8)/(-1 + 3) = -4/2 = -2

m = -2

And also we know that the line contains the point (2,3), using this point we can find the value of b:

y = mx + b

3 = (-2)(2) + b

3 = -4 + b

3 + 4 = b

b = 7

So the line equation with m = -2 and b = 7 is: y = -2x + 7

Answer: y = -2x + 7