<h3>
Answer: slope = 1/3</h3>
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Work Shown:
Use the slope formula to get
m = (y2 - y1)/(x2 - x1)
m = (0 - (-3))/(9 - 0)
m = (0 + 3)/(9 - 0)
m = 3/9
m = 1/3
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Basically we subtract the y coordinates, and do the same for the x coordinates as well (subtract in the same order). Afterward, divide the two results. Reduce the fraction as much as possible.
A slope of 1/3 means we move up 1 unit each time we move to the right 3 units.
The slope being positive means the line goes uphill as you read from left to right.
The given equation is

And we have to solve for y.
Solving for y, means isolating y . And to isolate y, we need to get rid of 4 that is with y .
It means we have to separate 4 from y, and for separation , we have to perform division. That is, we have to divide both sides by 4, and that will be the next step .
So out of the four options, correct option is the last option .
I believe there has to be an image included with this question my friend. Thine error hath been made known by the supreme lord of dao.
Based on the calculations, the measure of angle BDF and CFG are 100° and 38° respectively.
<h3>The condition for two parallel lines.</h3>
In Geometry, two (2) straight lines are considered to be parallel if their slopes are the same (equal) and they have different y-intercepts. This ultimately implies that, two (2) straight lines are parallel under the following conditions:
m₁ = m₂
<u>Note:</u> m is the slope.
<h3>What is the alternate interior angles theorem?</h3>
The alternate interior angles theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.
Based on the alternate interior angles theorem, we can infer and logically deduce the following properties from the diagram (see attachment):
For angle BDF, we have:
<BDF = <BDH + <HDF
<BDF = 38° + 62°
<BDF = 100°.
Since angles BDF and DFC are linear pair, they are supplementary angles. Thus, we have:
∠BDF + <DFC = 180°
<DFC = 180 - ∠BDF
<DFC = 180 - 100
<DFC = 80°.
For angle CFG, we have:
∠DFE + <DFC + <CFG= 180°
<CFG = 180° - ∠DFE - <DFC
<CFG = 180° - 62° - 80°
<CFG = 38°.
Read more on parallel lines here: brainly.com/question/3851016
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