Answer & Step-by-step explanation:
When two lines are parallel, their slopes are the same. To find the slope of the given equation, convert to slope-intercept form:
[tex]y=mx+b\\\\[/tex]
[tex]6x-5y=15[/tex]
Solve for y. Subtract 6x from both sides:
[tex]6x-6x-5y=15-6x\\\\-5y=-6x+15[/tex]
Divide both sides by -5:
[tex]\frac{-5y}{-5} =\frac{-6x}{-5} +\frac{15}{-5} \\\\y=\frac{6}{5}x-3[/tex]
The slope is [tex]\frac{6}{5}[/tex].
Now you need to make an equation in point-slope form:
[tex]y-y_{1}=m(x-x_{1})[/tex]
Insert known values:
[tex]y-4=\frac{6}{5}(x-5)[/tex]
You can use this equation, or you can convert to slope-intercept form by solving for y:
Use the distributive property:
[tex]y-4=\frac{6}{5} x-6[/tex]
Add 4 to both sides:
[tex]y-4+4=\frac{6}{5}x-6+4\\\\ y=\frac{6}{5}x-2[/tex]
:Done
The equation of the perpendicular line is [tex]y = \frac 65x - 2[/tex]
The equation of the line is given as:
[tex]6x -5y = 15[/tex]
Start by calculating the slope (m) of the line as follows:
[tex]6x -5y = 15[/tex]
Subtract 6x from both sides
[tex]-5y = 15 - 6x[/tex]
Divide both sides of the equations by -5
[tex]y = -3 + \frac65x[/tex]
Rewrite as:
[tex]y = \frac65x-3[/tex]
For a linear equation, y = mx + b, the slope of the line is m
So, the slope is:
[tex]m = \frac65[/tex]
The equation of the line is said to be parallel to the above equation
So, the slope of the line is:
[tex]m = \frac65[/tex]
The line is said to pass through point (5,4).
So, the equation of the line is:
[tex]y = m(x - x_1) +y_1[/tex]
This gives
[tex]y = \frac 65(x - 5) +4[/tex]
Expand
[tex]y = \frac 65x - 6 +4[/tex]
[tex]y = \frac 65x - 2[/tex]
Hence, the equation of the line is [tex]y = \frac 65x - 2[/tex]
Read more about line equations at:
https://brainly.com/question/14323743
