The question illustrates linear equation
- The equation in point slope form is: [tex]\mathbf{ y - 1 = \frac 35 (x - 6)}[/tex]
- The equation in slope intercept form is: [tex]\mathbf{ y = \frac 35x - \frac{13}5}[/tex]
The given parameters are:
[tex]\mathbf{m = \frac 35}[/tex] --- the slope
[tex]\mathbf{(x_1,y_1) = (6,1)}[/tex] -- the point it passes through
(a) The equation in point slope form
This is represented as:
[tex]\mathbf{ y - y_1 = m(x - x_1)}[/tex]
Substitute known values
[tex]\mathbf{ y - 1 = \frac 35 (x - 6)}[/tex]
So, the equation in point slope form is: [tex]\mathbf{ y - 1 = \frac 35 (x - 6)}[/tex]
(a) The equation in slope intercept form
In (a), we have:
[tex]\mathbf{ y - 1 = \frac 35 (x - 6)}[/tex]
Open brackets
[tex]\mathbf{ y - 1 = \frac 35x - \frac{18}5}[/tex]
Add 1 to both sides
[tex]\mathbf{ y = \frac 35x - \frac{18}5 + 1}[/tex]
Take LCM
[tex]\mathbf{ y = \frac 35x + \frac{-18 + 5}5}[/tex]
[tex]\mathbf{ y = \frac 35x + \frac{-13}5}[/tex]
[tex]\mathbf{ y = \frac 35x - \frac{13}5}[/tex]
Hence, the equation in slope intercept form is: [tex]\mathbf{ y = \frac 35x - \frac{13}5}[/tex]
Read more about linear equations at:
https://brainly.com/question/11897796
