Question

Write an equation in point-slope form and slope-intercept form for a line passes through (0, 1) and (2, 5)

1-y - 5 = 2 ( x + 2 ) ; y= 2x - 1
2-y + 5 = 2 ( x - 2 ) ; y = 2x - 1
3-y - 2 = 5 ( x - 2 ) ; y=5x + 1
4-y - 5 = 2(x - 2) ; y = 2x + 1
pls fast

Answer 1

4) y - 5 = 2 (x -2) ;y = 2 x +1

The equation of the straight line in point - slope form

y - 5 = 2 (x -2)

The equation of the straight line passing through the point (2,5) and having slope m=2

y = 2 x +1

Explanation:

Step(i):-

Given that the points are (0,1) and (2,5)

Slope of the line

`m = (y_(2)-y_(1) )/(x_(2) -x_(1) ) = (5-1)/(2-0) = (4)/(2) = 2`

Step(ii):-

The equation of the straight line passing through the point (2,5) and having slope m=2

y - y₁ = m(x-x₁)

y - 5 = 2 (x -2)

y -5 = 2x - 4

y = 2x -4+5

y = 2 x +1

Final answer:-

The equation of the straight line in point - slope form

y - 5 = 2 (x -2)

The equation of the straight line passing through the point (2,5) and having slope m=2

y = 2 x +1