Chapter 4

Explain how to solve a linear equation in one variable graphically.

In the ordered pair \((4,9),\) the \(x\) -coordinate is ______ $

Is every function a relation? Is every relation a function? Explain.

Explain what it means for x and y to vary directly.

Why is the equation \(y=m x+b\) called the slope-intercept form?

Draw a ramp and label its rise and run. Explain what is meant by the slope of the ramp.

Decide whether 2 is the \(x\) -intercept or the \(y\) -intercept of the line \(y=2 x+2\) Explain your choice.

Complete the following sentence: An ordered pair that makes an equation in two variables true is called a(n) _____.

In Example \(2,\) explain why the \(x\) -intercept of the line \(y=-\frac{2}{3} x+3\) is the solution of the equation \(0=-\frac{2}{3} x+3\).

Decide whether the following statement is true or false. Each point in a coordinate plane corresponds to an ordered pair of real numbers.

Describe a line that cannot be the graph of a linear function.

In a direct variation equation, how are the constant of variation and the slope related?

Explain how to graph \(2 x-3 y=6\) using slope-intercept form.

How many points are needed to determine a line?

Solve the equation graphically. Check your answer algebraically. $$x-3=7$$

Evaluate the function \(f(x)=3 x-10\) for the given value of \(x .\) $$ x=0 $$

Graph the equation. State whether the two quantities have direct variation. If they have direct variation, find the constant of variation and the slope of the direct variation model. $$y=x$$

Explain what happens when the formula for slope is applied to a vertical line.

Decide whether the graphs of \(y=x+2\) and \(y=x-4\) are parallel lines.

Describe a line that has no \(x\) -intercept.

Decide whether the following statement is true or false. The graph of the equation \(x=3\) is a horizontal line. Explain.

Solve the equation graphically. Check your answer algebraically. $$2-x=-5$$

Plot the ordered pairs in a coordinate plane. (GRAPH CANNOT COPY) $$A(4,-1), B(5,0)$$

Evaluate the function \(f(x)=3 x-10\) for the given value of \(x .\) $$ x=20 $$

Graph the equation. State whether the two quantities have direct variation. If they have direct variation, find the constant of variation and the slope of the direct variation model. $$y=4 x$$

How can you tell that the slope of the line through \((2,2)\) and \((-3,5)\) is negative without calculating?

Find the \(x\) -intercept of the graph of the equation. $$ y=2 x+20 $$

Use a table of values to graph the equation. \(6 x-3 y=12\)

Solve the equation graphically. Check your answer algebraically. $$5 x+6=-9$$

Plot the ordered pairs in a coordinate plane. (GRAPH CANNOT COPY) $$A(-2,-3), B(-3,-2)$$

Evaluate the function \(f(x)=3 x-10\) for the given value of \(x .\) $$ x=-2 $$

Graph the equation. State whether the two quantities have direct variation. If they have direct variation, find the constant of variation and the slope of the direct variation model. $$y=\frac{1}{2} x$$

Plot the points and draw a line through them. Find the slope of the line passing through the points. $$(0,0),(1,2)$$

Find the slope and the y-intercept of the graph of the equation. $$ y=2 x+1 $$

Find the \(x\) -intercept of the graph of the equation. \(y=0.1 x+0.3\)

Use a table of values to graph the equation. \(x=1.5\)

Match the one-variable equation with its related function. $$2 x=10$$ A. \(y=2 x-16\) B. \(y=-2 x-11\) c. \(y=2 x-10\) D. \(y=2 x-1\) E. \(y=18 x+3\)

Plot the ordered pairs in a coordinate plane. (GRAPH CANNOT COPY) The point \((-2,5)\) lies in Quadrant \(\underline{?}\).

Evaluate the function \(f(x)=3 x-10\) for the given value of \(x .\) $$ x=\frac{2}{3} $$

Graph the equation. State whether the two quantities have direct variation. If they have direct variation, find the constant of variation and the slope of the direct variation model. $$y=2 x$$

Plot the points and draw a line through them. Find the slope of the line passing through the points. $$(0,0),(-1,-1)$$

Find the slope and the y-intercept of the graph of the equation. $$ y=11 x $$

Find the \(x\) -intercept of the graph of the equation. $$ y=x-\frac{1}{4} $$

Use a table of values to graph the equation. \(y=-2\)

Match the one-variable equation with its related function. $$2 x-10=6$$ A. \(y=2 x-16\) B. \(y=-2 x-11\) c. \(y=2 x-10\) D. \(y=2 x-1\) E. \(y=18 x+3\)

Draw a scatter plot of the given data. $$\begin{array}{|l|c|c|c|c|}\hline \text { Time } & 1: 00 & 3: 00 & 5: 00 & 7: 00 \\ \hline \text { Temp. } & 71^{\circ} & 74^{\circ} & 68^{\circ} & 63^{\circ} \\\\\hline\end{array}$$

Graph the equation. State whether the two quantities have direct variation. If they have direct variation, find the constant of variation and the slope of the direct variation model. $$y=x-4$$

Plot the points and draw a line through them. Find the slope of the line passing through the points. $$(1,2),(2,1)$$

Find the slope and the y-intercept of the graph of the equation. $$ y=x+3 $$

Find the \(x\) -intercept and the \(y\) -intercept of the graph of the equation. Graph the equation. $$ y=x+2 $$