Question

Write an equation in point-slope form and slope-intercept form for each line.

Answer 1

Step-by-step explanation:

Point slope-form of a line passing through the point $(x_0, y_0)$ and having m is $y-y_0=m(x-x_0)\cdots(i)$

The slope-intercept form of a line having slope m and y-intercept c is

$y=mx+c\cdots(ii)$

(1). The line is passing through $(x_0, y_0)=(-5,6)$ and having the slope m=3.

So, by using equation (i), the point-slope form of the line is

$y-6=3(x-(-5))$

$\Rightarrow y-6=3(x+5)$

By using equation (ii), the slope-intercept form of the line is

$y=3x+c\cdots(iii)$

as the line is passing through the point (-5,6), so pout this point in the equation (iii) to get the value of c.

$6=3\times(-5)+c$

$\Rightarrow 6=-15+c$

$\Rightarrow c=6+15=21$

From equation (iii), the slope-intercept form of the line is $y=3x+21$.

(2). The line is passing through the points (–5, 9) and (1, 3).

As two points are given, so the slope of the line is

$m=\frac{3-9}{1-(-5)}=-1.$

Now, proceeding in the same way as in part (1),

By using equation (i), the point-slope form of the line is

$y-3=-1(x-1)$ [taking point (1,3) and m=-1]

By using equation (ii), the slope-intercept form of the line is

$y=(-1)x+c\cdots(iv)$

as the line is passing through the point (1,3), so pout this point in the equation (iv) to get the value of c.

$3=-1\times1+c$

$\Rightarrow 3=-1+c$

$\Rightarrow c=3+1=4$

From equation (iv), the slope-intercept form of the line is y=-x+4.