Respuesta :
Answer: 2/3 x+7 1/2=y
Step-by-step explanation:
-1/3 x+2y=15
-1/3 x-15=-2y
2/3 x+7 1/2=y
Answer:
[tex]y-2=\frac{2}{3} (x-5)[/tex]
Step-by-step explanation:
Pre-Solving
We are given that a line is perpendicular to 3x + 2y = 15 and passes through (5,2). We want to write the equation of this line.
Perpendicular lines have slopes that multiply to equal -1.
So, we need to first find the slope of 3x + 2y = 15
Notice how the line is in standard form, which is ax + by = c. The slope of the line when the equation is in standard form is [tex]-\frac{a}{b}[/tex].
Since a = 3 and b = 2, the slope of the line is [tex]-\frac{3}{2}[/tex].
Now, we want to find the slope of the line perpendicular to this line.
Since the two slopes multiply to equal -1,
[tex]-\frac{3}{2} * m_2 = -1[/tex]
Multiply both sides by [tex]-\frac{2}{3}[/tex].
We get:
[tex]m_2=\frac{2}{3}[/tex]
Now, there are three ways to write the equation of the line:
- Slope-intercept form, which is y = mx+b, where m is the slope and b is the value of y at the y -intercept.
- Standard form, which is ax+by=c, where a, b, and c are free integer coefficients.
- Point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1,y_1)[/tex] is a point.
As the question doesn't specify which form to use, any of the forms should work. However, let's use point-slope form, as that is the easiest form for us to use.
Solving
As we have found the slope and we were given a point, we can substitute these values into the formula.
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-2=\frac{2}{3} (x-5)[/tex]
