Question

to make soap, 12 grams of sodium hydroxide are added for every 100 milliliters of used cooking oil. which equation shows the relationship between these ingredients? let x represent the amount of sodium hydroxide, in grams, and y represent the amount of used cooking oil, in milliliters.
slope intercept form: ( y = \frac{25}{3}x )
slope intercept form: ( y = \frac{3}{25}x )
point slope form: ( y - 0.5 = \frac{25}{3}(x - 4) )
point slope form: ( y - 0.5 = \frac{3}{25}(x - 4) )
question 2
1 point
on a map, spruce city lies on the coordinate ( (0, 7) ). tortoise town is to the northeast, up 18 units, and 3 to the right. which equation best describes the line that passes through both places?
( y = 6x + 7 )
none of these equations describes a line that will go through both places.
( 6x + y = 7 )
( y - 7 = 3(x - 6) )

Explanation:

Question 1

Step1: Define ratio relationship

We know 13g of sodium hydroxide ($x$) corresponds to 100mL of oil ($y$). The ratio of oil to sodium hydroxide is $\frac{y}{x} = \frac{100}{13}$.

Step2: Rearrange to slope-intercept form

Rearrange the ratio to solve for $y$:
$y = \frac{100}{13}x$

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Question 2

Step1: Find second point coordinates

Start at $(0,7)$. Move 3 right (x increases by 3) and 18 up (y increases by 18), so the second point is $(0+3, 7+18) = (3,25)$.

Step2: Calculate slope

Slope $m = \frac{25-7}{3-0} = \frac{18}{3} = 6$.

Step3: Write slope-intercept equation

The y-intercept $b=7$ (from the point $(0,7)$). Substitute into $y=mx+b$:
$y = 6x + 7$

Answer:

Slope intercept form: $y = \frac{100}{13}x$