Master Algebra 1 Word Problems with our Comprehensive Practice

Write the equation in point slope form given (4, -5), perpendicular to 2x-5y= -10

Write the equation in point slope form given (4,5) and (-3,8)

Graph the line that passes through (4,-2) perpendicular to the graph 3x−2y=6

Find the equation of the line that passes through the origin and is perpendicular to the line that passes through the following points: (9,2),(−2,8)

Find a standard form equation for the line with point (2, 5) and is perpendicular to the line 4x + 9y − 7

Is 10, 5, 2.5, 1.25, 0.625, 0.3125 a geometric sequence?

Quadratic Bézier curve points
A quadratic Bézier curve is the path traced by the function B(t), given points $P_0$, $P_1$, and $P_2$.
$C(t)=\underset{i=0}{\overset{2}{\sum <!--\; \sum \; -->}}(\genfrac{}{}{0ex}{}{2}{i})t^i(1-<!--\; -\; -->t{)}^{2-<!--\; -\; -->i}{P}_i$
$C(t)=(P_0-<!--\; -\; -->2P_1+P_2)t^2+(-<!--\; -\; -->2P_0+2P_1)t+P_{0}t\in <!--\; \in \; -->[0,1]$
What exactly is $P_0$ or $P_1$ or $P_2$ concerning this equation?
Yes they are points. But in my understanding, a point is a pair of numbers (in 2D-space).
Let $=(1,1)$, $P_1=(1,7)$ and $P_2=(7,1)$.
What values do you use (and where)?
How do you calculate the Bezier Curve for these points?

How do you graph y=6−1.25x?

Determining quadratic function of this word problem
A tour company offers back country hiking excursions at $160 per person forgroups up to 50. For groups larger than 50, the company will reduce the cost of every ticket by $2 for each person in excess of 50. What size of group would produce the greatest revenue?
I'm not worried about finding out what the size of the group is that produces the greatest revenue. What I want to know is what the equation for this is. I was able to figure out this equation:
$f(x)=160x-<!--\; -\; -->2(x-<!--\; -\; -->50),$
where x is the number of people and f(x) is the revenue. But that's a linear function and we're doing quadratic functions. So, There should be an exponent and I'm thinking there's more to this question than I see? Or is it a linear function?

How do you write the point slope form of the equation given (1,-3) and slope 0?

Find the term n=13, given ${\displaystyle a_1=-5}$ and d=7

Find the slope that is perpendicular to the line ${\displaystyle y=\frac{7}{5}x-2}$

Write the point slope form of the equation given (-4,0) parallel to ${\displaystyle y=\frac{3}{4}x-2}$

Ben was walking in Manhattan at a constant speed. He went along 5th avenue from 4th to 98th street. At 3:00 he was on 15th street, and at 4:30 he was on 45th street. When did he start and when did he finish his walk?

Write the rule for the nth term given 1,10,100,1000,...

How is discriminant related to real x?
Solve for range of the function,
$y=\frac{x^2+4x-<!--\; -\; -->1}{3x^2+12x+20}$
Text book says, cross multiply and express the obtained equation as a quadratic equation in x
So I get $(3y-<!--\; -\; -->1)x^2+(12y-<!--\; -\; -->4)x+(20y-<!--\; -\; -->1)=0$
Now it says find discriminant D, so we have,
$D=-<!--\; -\; -->4(3y-<!--\; -\; -->1)(8y+3)$
Now it says, set $D\ge 0$ as x is real. Wait what?
Isn't $x\in <!--\; \in \; -->\mathbb{R}$ the domain for a quadratic function? Meaning "x" is always real? What does a discriminant got anything to do with x being real, when all discriminant tells us is whether or not the ROOTS are real? Help please.
To be more specific about my doubt, here's an edit.

Solve a system of two equations in which the existence of $ln\left(\frac{\mathrm{\alpha <!--\; \alpha \; -->}}{\mathrm{\alpha <!--\; \alpha \; -->}+\mathrm{\beta <!--\; \beta \; -->}}\right)$ function makes some limitations in iterations of the Newton-Raphson method.
$\begin{array}{r}\{\begin{array}{l}ln\left(\frac{\mathrm{\alpha <!--\; \alpha \; -->}}{\mathrm{\alpha <!--\; \alpha \; -->}+\mathrm{\beta <!--\; \beta \; -->}}\right)-<!--\; -\; -->c_{s1}+\underset{i\in <!--\; \in \; -->A}{\sum <!--\; \sum \; -->}{c}_i({\mathrm{\alpha <!--\; \alpha \; -->}}^{-<!--\; -\; -->i}-<!--\; -\; -->(\mathrm{\alpha <!--\; \alpha \; -->}+\mathrm{\beta <!--\; \beta \; -->}{)}^{-<!--\; -\; -->i})\\ ln\left(\frac{\mathrm{\beta <!--\; \beta \; -->}}{\mathrm{\alpha <!--\; \alpha \; -->}+\mathrm{\beta <!--\; \beta \; -->}}\right)-<!--\; -\; -->c_{s1}+\underset{i\in <!--\; \in \; -->A}{\sum <!--\; \sum \; -->}{c}_i({\mathrm{\beta <!--\; \beta \; -->}}^{-<!--\; -\; -->i}-<!--\; -\; -->(\mathrm{\alpha <!--\; \alpha \; -->}+\mathrm{\beta <!--\; \beta \; -->}{)}^{-<!--\; -\; -->i})\end{array}\end{array}$

Write the first five terms of the arithmetic sequence given ${\displaystyle a_8=26,a_{12}=42}$

A geometric sequence is defined recursively by an = 4an-1. The 10th term of the sequence is a10 = 3.5. What is a13?

Find the point-slope form of the equation of the line passing through the point (-1, -3) and has slope 5