can you help me with math please

Question

Find an equation of the line that satisfies the given conditions.
Through (1, 9); parallel to the line passing through (2, 7) and (−2, 3)

Answer 1

parallel lines have similar slope, and we need at least two points to find a slope (in fact for each line we need at least two points)

(slope)m=(y2-y1)/(x2-x1)=(7-3)/(2-(-2))=1

 

In general, the equation of a line is Y=mx+b which b is called intercept and can be calculated by plugging the given point in the general equation. remember m=1

Y=X+b ==> 9=1+b ==>b=8

 

Y=X+8 is the equation of the line that passes through (1,9) and is parallel to the line passing through (2, 7) and (−2, 3)

Answer 2

This is a point slope problem. You are given a point on a line, but not the slope. However, the line is parallel to another line, and by definition they have the same slope. So figure out the slope of the second line and use it with the point given for the first line. The slope formula is (y2-y1)/(x2-x1). Plug in the values for the second line and (3-7)/(-2-2) is the slope, or m = -4/-4, and the slope is equal to 1. Now use the point slope formula. y - y1 = m(x - x1) Plug in the numbers, y - 9 =1(x - 1). Add 9 to both sides and y = x + 8. Hope that helps.

I mistyped one of the x values in my original answer and have corrected it. My apologies.

Answer 3

The slope of the given line is (7 - 3)/(2 - (-2)) = 4/4 = 1.

 

Parallel lines have the same slope.

 

y - 9 = 1(x - 1)

y - 9 = x - 1

y = x + 8