Question

for which instances would point - slope form be the best equation for a linear function? select all that apply. \\(m = 3, (4,5)\\) \\((-8,9),(2,8)\\) \\(m = 0, (0,1)\\) the \\(x\\)-intercept is \\((-7,0)\\) and the \\(y\\)-intercept is \\((0,3)\\) \\(\text{question 2}\\) \\(1\\ \text{point}\\) a t - shirt company produces plain t - shirts for \\$15 each and printed t - shirts for \\$45 each. if they make \\(x\\) plain t - shirts and \\(y\\) printed t - shirts, and their total revenue is \\$135. which form of equation will give us the \\(x\\)- and \\(y\\)-intercepts with the least number of addition or subtraction calculations, and what is the equation? \\(\circ\\) standard form; the equation is \\(15x + 45y = 135\\) \\(\circ\\) standard form; the equation is \\(45x - 15y = 135\\) \\(\circ\\) slope - intercept form; the equation is \\(y = \frac{1}{3}x + 3\\) \\(\circ\\) slope - intercept form; the equation is \\(y = - 3x + \frac{1}{3}\\)

Explanation:

First Question

Point-slope form $y-y_1=m(x-x_1)$ is best when given either a slope and a single point, or two points (to calculate slope first). The first option gives a slope and a point. The second option gives two points, from which slope can be derived. The third option (slope 0 and y-intercept point) is better suited for slope-intercept form, and the fourth option (two intercepts) is better suited for intercept or standard form.

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Second Question

Step1: Define revenue variables

Revenue from plain shirts: $15x$, revenue from printed shirts: $45y$. Total revenue = $135$.

Step2: Build total revenue equation

$$15x + 45y = 135$$

Step3: Compare form suitability

Standard form $Ax+By=C$ allows direct calculation of intercepts with minimal arithmetic: set $x=0$ to find $y$-intercept, set $y=0$ to find $x$-intercept, requiring only division after isolating the variable. Slope-intercept form requires more rearrangement steps to find both intercepts.

Answer:

• $m = 3, (4,5)$
• $(-3,9),(2,6)$