Outro W5

Revie of the week

You can find the key concepts you studied this week in the following short reviews

4.5 Use the Slope-Intercept Form of an Equation of a Line

The slope–intercept form of an equation of a line with slope $m$ and y-intercept, $(0, b)$ is, $y = m x + b$ .
Graph a Line Using its Slope and y-Intercept
1. Step 1. Find the slope-intercept form of the equation of the line.
2. Step 2. Identify the slope and y-intercept.
3. Step 3. Plot the y-intercept.
4. Step 4. Use the slope formula $LaTeX: m=\frac{rise}{run}$ $m=\frac{rise}{run}$ to identify the rise and the run.
5. Step 5. Starting at the y-intercept, count out the rise and run to mark the second point.
6. Step 6. Connect the points with a line.

Strategy for Choosing the Most Convenient Method to Graph a Line: Consider the form of the equation.
- If it only has one variable, it is a vertical or horizontal line.
  $x = a$ is a vertical line passing through the x-axis at $a$ .
  $y = b$ is a horizontal line passing through the y-axis at $b$ .
- If $y$ is isolated on one side of the equation, in the form $y = m x + b$ graph by using the slope and y-intercept.
  Identify the slope and y-intercept and then graph.
- If the equation is of the form $A x + B y = C$ , find the intercepts.
  Find the x- and y-intercepts, a third point, and then graph.
Parallel lines are lines in the same plane that do not intersect.
- Parallel lines have the same slope and different y-intercepts.
- If m₁ and m₂ are the slopes of two parallel lines then $m_1=m_2$ $m_{1} = m_{2} .$
- Parallel vertical lines have different x-intercepts.
Perpendicular lines are lines in the same plane that form a right angle.
- If $LaTeX: m_1\:and\:m_2$ $m_1\:and\:m_2$ are the slopes of two perpendicular lines, then $LaTeX: m_1\cdot m_2=-1$ $m_1\cdot m_2=-1$ and $LaTeX: m_1=-\frac{1}{m_2}$ $m_1=-\frac{1}{m_2}$ .
- Vertical lines and horizontal lines are always perpendicular to each other.

4.6 Find the Equation of a Line

To Find an Equation of a Line Given the Slope and a Point
1. Step 1. Identify the slope.
2. Step 2. Identify the point.
3. Step 3. Substitute the values into the point-slope form, $LaTeX: y-y_1=m\left(x-x_1\right)$ $y-y_1=m\left(x-x_1\right)$ .
4. Step 4. Write the equation in slope-intercept form.
To Find an Equation of a Line Given Two Points
1. Step 1. Find the slope using the given points.
2. Step 2. Choose one point.
3. Step 3. Substitute the values into the point-slope form, $LaTeX: y-y_1=m\left(x-x_1\right)$ $y-y_1=m\left(x-x_1\right)$ .
4. Step 4. Write the equation in slope-intercept form.
To Write and Equation of a Line
- If given slope and y-intercept, use slope–intercept form $y=mx+b$ .
- If given slope and a point, use point–slope form $LaTeX: y-y_1=m\left(x-x_1\right)$ $y-y_1=m\left(x-x_1\right)$ .
- If given two points, use point–slope form $LaTeX: y-y_1=m\left(x-x_1\right)$ $y-y_1=m\left(x-x_1\right)$ .
To Find an Equation of a Line Parallel to a Given Line
1. Step 1. Find the slope of the given line.
2. Step 2. Find the slope of the parallel line.
3. Step 3. Identify the point.
4. Step 4. Substitute the values into the point-slope form, $LaTeX: y-y_1=m\left(x-x_1\right)$ $y-y_1=m\left(x-x_1\right)$
5. Step 5. Write the equation in slope-intercept form.
To Find an Equation of a Line Perpendicular to a Given Line
1. Step 1. Find the slope of the given line.
2. Step 2. Find the slope of the perpendicular line.
3. Step 3. Identify the point.
4. Step 4. Substitute the values into the point-slope form, $LaTeX: y-y_1=m\left(x-x_1\right)$ $y-y_1=m\left(x-x_1\right)$ .
5. Step 5. Write the equation in slope-intercept form.

4.7 Graphs of Linear Inequalities

To Graph a Linear Inequality
1. Step 1. Identify and graph the boundary line.
  If the inequality is $\leq or \geq$ , the boundary line is solid.
  If the inequality is < or >, the boundary line is dashed.
2. Step 2. Test a point that is not on the boundary line. Is it a solution of the inequality?
3. Step 3. Shade in one side of the boundary line.
  If the test point is a solution, shade in the side that includes the point.
  If the test point is not a solution, shade in the opposite side.

5.1 Solve Systems of Equations by Graphing

To solve a system of linear equations by graphing
1. Step 1. Graph the first equation.
2. Step 2. Graph the second equation on the same rectangular coordinate system.
3. Step 3. Determine whether the lines intersect, are parallel, or are the same line.
4. Step 4. Identify the solution to the system.
  If the lines intersect, identify the point of intersection. Check to make sure it is a solution to both equations. This is the solution to the system.
  If the lines are parallel, the system has no solution.
  If the lines are the same, the system has an infinite number of solutions.
5. Step 5. Check the solution in both equations.
Determine the number of solutions from the graph of a linear system
Determine the number of solutions of a linear system by looking at the slopes and intercepts
Determine the number of solutions and how to classify a system of equations
Problem Solving Strategy for Systems of Linear Equations
1. Step 1. Read the problem. Make sure all the words and ideas are understood.
2. Step 2. Identify what we are looking for.
3. Step 3. Name what we are looking for. Choose variables to represent those quantities.
4. Step 4. Translate into a system of equations.
5. Step 5. Solve the system of equations using good algebra techniques.
6. Step 6. Check the answer in the problem and make sure it makes sense.
7. Step 7. Answer the question with a complete sentence.

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