Question

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

Answer 1

Answer:

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

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

3. $y-1=\frac{1}{2}(x+4)$

4. $y+5=-\frac{4}{5}(x-5)$

5. $y-0=-\frac{1}{3}(x+1)$

Step-by-step explanation:

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

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

We know that,

The slope of the line is,

$m=\frac{y_2-y_1}{x_2-x_1}$

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

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),

$y-1=\frac{2-1}{-4+5}(x+5)$

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

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

$y-1=\frac{2-1}{0+4}(x+4)$

$y-1=\frac{1}{2}(x+4)$

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,

$y+5=-\frac{4}{5}(x-5)$

5. If a line has slope m then the slope of perpendicular line is $-\frac{1}{m}$

Slope of line y = x + 3,

Slope of perpendicular line of y = x + 3 = -$\frac{1}{3}$,

So, the equation of line passes through (-1, 0) with slope $-\frac{1}{3}$,

$y-0=-\frac{1}{3}(x+1)$

Answer 2

Answer:

all steps in the picture above