Pt Slope Formula
The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept. If you a point that a line passes through, and its slope, this page will show you how to find the equation of the line. Point Slope Form Formula. The other popular format for straight line equations is point slope formula. For this purpose, you need to find out the values (x1, y1) and a slope m. Further, plug the values into the formula –.
What is the Slope?
The slope of a line in the two-dimensional Cartesian coordinate plane is usually represented by the letter $m$, and it is sometimes called underline{the rate of change} between two points. This is because it is the change in the $y$-coordinates divided by the corresponding change in the $x$ -coordinates between two distinct points on the line. If we have coordinates of two points $A(x_A,y_A)$ and $B(x_B,y_B)$ in the two-dimensional Cartesian coordinate plane, then the slope $m$ of the line through $A(x_A,y_A)$ and $B(x_B,y_B)$ is fully determined by the following formula$$m=frac{y_B-y_A}{x_B-x_A}$$In other words, the formula for the slope can be written as$$m=frac{Delta y}{Delta x}=frac{{rm vertical ; change}}{{rm horizontal ; change}}=frac{{rm rise}}{{rm run}}$$As we know, the Greek letter $Delta$, means difference or change. The slope $m$ of a line $y=mx+b$ can be defined also as the rise divided by the run.Rise means how high or low we have to move to arrive from the point on the left to the point on the right, so we change the value of $y$. Therefore, the rise is the change in $y$, $Delta y$. Run means how far left or right we have to move to arrive from the point on the left to the point on the right, so we change the value of $x$. The run is the change in $x$, $Delta x$.
The slope $m$ of a line $y=mx+b$ describes its steepness. For instance, a greater slope value indicates a steeper incline.There are four different types of slope:- Positive slope $m>0$, if a line $y=mx+b$ is increasing, i.e. if it goes up from left to right;
- Negative slope $m<0$, if a line $y=mx+b$ is decreasing, i.e. if it goes down from left to right;
- Zero slope, $m=0$, if a line $y=mx+b$ is horizonal. In this case, the equation of the line is$y=b$;
- Undefined slope, if a line $y=mx+b$ is vertical. This is because division by zero leads to infinities. So, the equation of the line is $x=a$. All vertical lines $x=a$ have an infinite or undefined slope.
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This exclusive ensemble of printable worksheets has been designed to help 8th grade and high school learners comprehend the basics of converting equation of a line to point-slope form and writing equation of a line using the given point and the slope. A series of exercises requires students to find the equations of a line that is either parallel or perpendicular to another equation of the line. The pdf worksheets based on graphing the line using a point and the slope are also included. Access some of these worksheets for free!
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Write the equation of a line in point-slope form based on the slope and the point provided in this set of printable worksheets. There are ten problems in each worksheet.
Point Slope Formula Worksheet
Based on the point and the slope provided for each question, apply point-slope formula to find the equation of a line and express the equation in slope-intercept form: y = mx + b. This level of worksheets features coordinates in the form of integers, and the slope provided can either be an integer or a fraction.
In the second level of worksheets, the coordinates are represented as fractions and the slopes are either in the form of integers or simplified fractions. Find the equation of a line and write the equation in slope-intercept form.
Find the equation of a line based on the given slope and a point and express the equation in standard form. The slopes in this collection of grade 8 and high school pdf worksheets can be in the form of either integers or fractions whereas the coordinates are represented in integer form.
In this second level of worksheets, the coordinates are given as fractions and the slopes can be either in the form of fractions or integers. Apply point-slope formula and find the equation of a line. Represent the equation of a line in standard form ax + by = c.
Find the equation of a line that is passing through the given point and is either parallel or perpendicular to another line. Write the equation of a line in standard form. Download these worksheets for ample practice.
Use this exclusive set of printable worksheets to graph the line based on the point and the slope provided. Plot the given point, mark another point on the grid using the given slope and graph the line. Use the answer key to verify your responses.
Related Worksheets
»Two-point Form
Point Slope Form Ppt
»Equation of a Line