Answer:
a) y = 3x+12
b) y-6 = 3(x+2)
Step-by-step explanation:
The equation of a line in slope-intercept form is expressed as y = mx+c
m is the slope or gradient
c is the intercept
We need to calculate the value of slope and intercept.
We will get the slope from the equation of line x+3y = 7
Rewriting the equation
3y = 7-x
y = 7/3 -x/3
M = -1/3
Since the equation if the unknown line is perpendicular to this line then Mm = -1 where m is the slope of the unknown line
m = -1/M
m = -1/(-1/3)
m = 3
To get c, we will substite the point given (-2,6) and the slope into the equation y = mx+c
6 = 3(-2)+c
6 = -6+c
c = 12
Substituting m= 3 and c = 12 into the standard form of the equation we have;
y = 3x+12 (This gives the required equation in its slope intercept form)
b) The standard form of a line is expressed as y-y1 = m(x-x1) where (x1,y1) are the points and m is the slope. On substituting the point {-2,6) and slope of 3 into this equation we will have:
y - 6 = 3(x-(-2))
y-6 = 3(x+2)
This gives the equation of the line in its standard form
