Linear Equations

Solving a two-step equation with signed fractions Solve for $y$. \[ -\frac{1}{2} y-\frac{6}{5}=-\frac{4}{3} \] Simplify your answer as much as possible. \[ y= \]

$2 x=4\left(\frac{1}{4}-\frac{3}{4} x\right)-6$

3 What are the slope and \( y \)-intercept of the line that passes through the pair of points \( (5,1) \) and \( (-10,-11) \) ? (A) \( m=-3, b=\frac{4}{5} \) (B) \( m=\frac{4}{5}, b=-3 \) \( m=3, b=-\frac{4}{5} \) (D) \( m=-\frac{4}{5}, b=3 \)

$3 y-33=-3 x$

Rewrite the equation 5x - 3y = 7 in standard form.

Consider the equation $1.5 x+4.5 y=18$. 1 If we graph the equation, what is the slope of the graph? Where does the graph intersect the $y$-axis? Write as a coordir Where does it intersect the $\mathrm{x}$-axis? Write as a coordinate

A line passes through the point $(-9,1)$ and has a slope of -2 . Write an equation for this line.

The percent of births to teenage mothers that are out-of-wedlock can be approximated by a linear function of the number of years after 1953. The percent was 16 in 1970 and 72 in 2006 Complete parts (a) through (c) (a) What is the slope of the line joining the points $(17,16)$ and $(53,72)$ ? The slope of the line is 1.56. (Simplify your answer: Round to two decimal places as needed) (b) What is the average rate of change in the percent of teenage out-of-wedlock births over this period? The average rate of change in the percent of teenage out-of-wedlock births over this period is 1.56 . (Simplify your answer. Round to two decimal places as needed) (c) Use the slope from part (a) and the number of teenage mothers in 2006 to write the equation of the line The equation is $p=$ (Do not factor. Type an expression using $x$ as the variable)

Write an equation in slope-intercept form for the line with slope $-\frac{4}{3}$ and $y$-intercept 1 .

Find the constant \(b\) in the linear equation \(y=2x+b\) if the line passes through the point \((3,7)\)

If $f(x)$ is a linear function, $f(-4)=3$, and $f(4)=-1$, find an equation for $f(x)$

Write the equation of the line that is perpendicular to $y=-2 x+1$ and passes through $(4,-2)$

What is the slope of the line that passes through the points $(7,-4)$ and $(11,-4)$ ? Write your answer in simplest form.

Use the given conditions to write an equation for the line in slope-intercept form. Passing through $(-3,2)$ and parallel to the line whose equation is $y=\frac{2}{3} x+\frac{8}{3}$

Find the slope of a line parallel to the line whose equation is \( x+y=-7 \). Fully simplify your answer.

Find the equation of the line parallel to the line with equation \(2x - 3y = 5\) and passing through the point \((2, -1)\).

Find the slope of a line perpendicular to the line whose equation is \( 6 x+2 y=-32 \). Fully simplify your answer.

Find the equation of the line perpendicular to the line \(3x - 4y = 8\) and passes through the point \((2, -3)\).

(2) For the rule $y=3 x-4$, find the value of $y$ for these $x$-values. a $x=2$ b $x=-1$

Graph the line. \[ y=-5 x+6 \] Check

A line passes through the point $(-10,-7)$ and has a slope of $-\frac{1}{2}$. Write an equation in slope-intercept form for this line.