Answer:
[tex]y = \frac{3}{2}x-5[/tex]
Step-by-step explanation:
1) First, find the slope of the given line. Since the y is isolated in the equation and it is in a [tex]y = mx +b[/tex] format, it must be in slope-intercept form. Remember that the number in place of [tex]m[/tex], or the coefficient of the x-term, represents the slope of a line in slope-intercept form. So, the slope of the given line is [tex]-\frac{2}{3}[/tex].
Lines that are perpendicular have slopes that are opposite reciprocals. So, the slope of the new line will be [tex]\frac{3}{2}[/tex].
2) Now, use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] and substitute the appropriate values for [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex]. This gives the equation of the line in point-slope form. (We can convert it to slope-intercept form later.)
Since [tex]m[/tex] represents the slope, substitute [tex]\frac{3}{2}[/tex] in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of one point the line intersects, substitute the x and y values of (6,4) into the equation as well. With the resulting equation, isolate y to find the equation of the line in slope-intercept form:
[tex]y-4 = \frac{3}{2} (x-6)\\y-4 = \frac{3}{2} x-9\\y = \frac{3}{2}x-5[/tex]
