Notes
Questions
Express the equation of the line in slope-intercept form
\(\textbf{1)}\) \(3x+4y=12\)
\(\textbf{2)}\) \(2x-3y=9\)
\(\textbf{3)}\) Slope \(= 3\), \(\,\) y-intercept \(=7\)
\(\textbf{4)}\) Slope \(= -\displaystyle\frac{2}{3} \), \(\,\) y – intercept \(= 5\)
\(\textbf{5)}\) Line through points \((3,4)\) and \((5,8)\)
\(\textbf{6)}\) Graph \(y=-2x+3\)
\(\textbf{7)}\) Graph \(y=.5x+1.5\)
\(\textbf{8)}\) Find the x- and y- intercepts of \(y=3x+2\)
\(\textbf{9)}\) Find the slope of \(y=-3\)
\(\textbf{10)}\) Find the slope and y-intercept of \(y=4x\)
\(\textbf{11)}\) Find the slope and y-intercept of \(y=4\)
\(\textbf{12)}\) Find equation of the following line
\({\begin{array}{|c|c|c|c|c|c|}
\hline
\textbf{x} & 0 & 1 & 2 & 3 & 4 \\
\hline
\textbf{y} & 8 & 6 & 4 & 2 & 0 \\
\hline
\end{array} }
\)
See Related Pages\(\)
\(\bullet\text{ Graphing Linear Equations}\)
\(\,\,\,\,\,\,\,\,2x-3y=6 \) 
\(\bullet\text{ Slope Formula}\)
\(\,\,\,\,\,\,\,\,m=\frac{y_2-y_1}{x_2-x_1}\)
\(\bullet\text{ Net Change}\)
\(\,\,\,\,\,\,\,\,y_2-y_1\)
\(\bullet\text{ Point Slope Form}\)
\(\,\,\,\,\,\,\,\,y-y_1=m(x-x_1)\)
\(\bullet\text{ Parallel and Perpendicular Slope}\)
\(\,\,\,\,\,\,\,\,m_1=m+2,\,\,\,m_1=\frac{1}{m_2}\)
\(\bullet\text{ Distance Between a Point and a Line}\)
\(\,\,\,\,\,\,\,\,(3,4) \text{ and } y=\frac{3}{4}x−2\)
\(\bullet\text{Finding x- and y- intercepts}\)
\(\,\,\,\,\,\,\,\,y=2x+4\)
In Summary
Slope-intercept form is a way of representing linear equations in mathematics. In this form, a linear equation is written as y = mx + b, where m is the slope of the line and b is the y-intercept. This form is useful because it allows for easy interpretation of the equation and easy graphing of the line on a coordinate plane.
Slope-intercept form is typically covered in a high school algebra or geometry class.
Slope-intercept form can be used to determine the equation of a line given two points on the line. By using the two points to find the slope and then substituting the coordinates of one of the two points into the slope-intercept form, it is possible to solve for the equation of the line through the two points.
Some real world examples of linear equations include calculating the distance traveled by a car moving at a constant speed, the amount of money a person earns as a function of the number of hours they work, the number of units a company sells as a function of the price. Anything with a constant growth rate.
The concept of slope-intercept form was first developed by the French mathematician René Descartes in the 17th century. He is credited with introducing the use of coordinates to represent points in space, which paved the way for the development of graphing techniques.