Question

Write the point-slope form of the equation of the line through the given point with the given slope.

1. Through: (1,4) Slope = 4

Write the point-slope form of the equation of the line through the given points.

2. Through: (-5,1) and (-4,2)
3. Through: (-4,1) and (0,2)

Write the slope intercept form of the equation of the line described.

4. Through: (5,-5), Parallel to y=-4/5x-4
5. Through: (-1,0) perpendicular to y=x+3

Answer 1

all steps in the picture above

Answer 2

1.
`y-4=4(x-1)`

2.
`y-1=1(x+5)`

3.
`y-1=(1)/(2)(x+4)`

4.
`y+5=-(4)/(5)(x-5)`

5.
`y-0=-(1)/(3)(x+1)`

Explanation:

∵ The equation of a line passes through
`(x_1, y_1)` and
`(x_2, y_2)` is,

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

We know that,

The slope of the line is,

`m=(y_2-y_1)/(x_2-x_1)`

`\implies y-y_1=m(x-x_1)`

Which is the point slope form of a line,

1. Thus, the equation of line passes through (1, 4) with slope 4 is,

`y-4=4(x-1)`

2. The equation of line passes through (-5, 1) and (-4, 2),

`y-1=(2-1)/(-4+5)(x+5)`

`y-1=1(x+5)`

3. The equation of line passes through (-4, 1) and (0, 2),

`y-1=(2-1)/(0+4)(x+4)`

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

4. Now, two parallel lines having the same slope.

Thus, the slope of line parallel to y = -4/5x - 4 is, -4/5,

So, the equation of line passes through (5, -5) with slope -4/5 is,

`y+5=-(4)/(5)(x-5)`

5. If a line has slope m then the slope of perpendicular line is
`-(1)/(m)`

Slope of line y = x + 3,

Slope of perpendicular line of y = x + 3 = -
`(1)/(3)`,

So, the equation of line passes through (-1, 0) with slope
`-(1)/(3)`,

`y-0=-(1)/(3)(x+1)`