Question

Write the slope-intercept form of the equation of the line through the given points13) through: (5, 3) and (5, 4)14) through: (0, 4) and (2, 3)15) trough: (-1, 4) and (-4,-5)16) through: (-1, -2) and (-3,0)

Answer 1

The slope-intercept form of the linear equation is

y = m x + b, where

m is the slope

b is the y-intercept

If the x-coordinates of the two points are equal, that means the line is vertical

A vertical line has no slope

Its equation is x = a, where a is the x-coordinate of any point on the line

13) The two points are (5, 3) and (5, 4)

They have the same x-coordinates, then its equation is

x = 5

The rule of the slope is

`m=(y2-y1)/(x2-x1)`

(x1, y1) and (x2, y2) are two points on the line

The line passes through points (0, 4) and (2, 3)

x1 = 0 and y1 = 4

x2 = 2 and y2 = 3

Substitute them in the rule above to find m

`m=(3-4)/(2-0)=-(1)/(2)`

The equation is

`y=-(1)/(2)x+b`

b is the value of y at x = 0

at x = 0 y = 4

b = 4

The equation of the line is

`y=-(1)/(2)x+4`