A line passes through the points (-3,1) and (9,5) and is labeled line d. Construct two lines: A line that is parallel to the line d described above through the point (6,7) and is labeled line g A line that is perpendicular to line g through the point (-3,-3) and is labeled line f. What is the equation for line g? I really need help with this because I'm struggling

The equation of line g is y = x/3 + 5

Step-by-step explanation:

Given that the line d passes through the points (-3, 1) and (9, 5) we have the equation of line d in slope and intercept form., y = m·x + c found as follows;

Where;

(x₁, y₁) = (-3, 1)

(x₂, y₂) = (9, 5)

The line, d, in point-slope form is y - 1 = 1/3(x - (-3))

Which gives;

y - 1 = 1/3·x + 3/3

y = 1/3·x + 1 + 1 = 1/3·x + 2

Given that line g is parallel to line d, we have;

Slope of line g = slope of line d = 1/3

Therefore, the equation of line g passing through point ^6, 7) in point-slope form is y - 7 = 1/3(x - 6) which gives;

y = x/3 - 2 + 7 = x/3 + 5

The equation of line g is y = x/3 + 5

The line f  passing through point (-3, -3) is perpendicular to ling g, therefore, the slope = -1/m = -1(1/3) = -3

The point-slope form of the equation is y -(-3) = -3(x - (-3)) which gives;

y + 3 = -3·x - 9

Therefore, the equation of line f is y = -3·x - 9 - 3 = -3·x - 12

The equation of line f is y = -3·x - 12.

step-by-step explanation:

the shape,the size and the distance

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)