Summary Students learn about four forms of equations: They graph and complete problem sets for each, converting from one form of equation to another, and learning the benefits and uses of each.
We will assign a number to a line, which we call slope, that will give us a measure of the "steepness" or "direction" of the line. It is often convenient to use a special notation to distinguish between the rectan- gular coordinates of two different points.
We can designate one pair of coordinates by x1, y1 read "x sub one, y sub one"associated with a point P1, and a second pair of coordinates by x2, y2associated with a second point P2, as shown in Figure 7. Note in Figure 7. The ratio of the vertical change to the horizontal change is called the slope of the line containing the points P1 and P2.
This ratio is usually designated by m. Thus, Example 1 Find the slope of the line containing the two points with coordinates -4, 2 and 3, 5 as shown in the figure at the right. Solution We designate 3, 5 as x2, y2 and -4, 2 as x1, y1. Substituting into Equation 1 yields Note that we get the same result if we subsitute -4 and 2 for x2 and y2 and 3 and 5 for x1 and y1 Lines with various slopes are shown in Figure 7.
Slopes of the lines that go up to the right are positive Figure 7. And note Figure 7. However, is undefined, so that a vertical line does not have a slope.
In this case, These lines will never intersect and are called parallel lines. Now consider the lines shown in Figure 7. In this case, These lines meet to form a right angle and are called perpendicular lines.
In general, if two lines have slopes and m2: If we denote any other point on the line as P x, y See Figure 7.
In general let us say we know a line passes through a point P1 x1, y1 and has slope m. If we denote any other point on the line as P x, y see Figure 7. In Equation 2m, x1 and y1 are known and x and y are variables that represent the coordinates of any point on the line.
Thus, whenever we know the slope of a line and a point on the line, we can find the equation of the line by using Equation 2. Example 1 A line has slope -2 and passes through point 2, 4. Find the equation of the line. The slope and y-intercept can be obtained directly from an equation in this form.
Example 2 If a line has the equation then the slope of the line must be -2 and the y-intercept must be 8. Solution We first solve for y in terms of x by adding -2x to each member. We say that the variable y varies directly as x.
Example 1 We know that the pressure P in a liquid varies directly as the depth d below the surface of the liquid. In this section we will graph inequalities in two variables. That is, a, b is a solution of the inequality if the inequality is a true statement after we substitute a for x and b for y.
Thus, every point on or below the line is in the graph.Find the slope given a graph, two points or an equation. Write a linear equation in slope/intercept form.
Determine if two lines are parallel, perpendicular, or neither.
The slope of the first equation is and the slope of the second equation is Since the two slopes are not equal and are not negative reciprocals of each other, then. Linear functions: Write equation - Slope-intercept form: write an equation from a graph Lines in the coordinate plane - Graph a linear equation Lines in the coordinate plane - Equations of lines.
Determining the Equation of a Line From a Graph. Determine the equation of each line in slope intercept form. Checking Your Answers. Simplifying Exponents of Polynomials Worksheet Substitution Worksheet Simplifying Exponents of Variables Worksheet Algebra Worksheets List.
using Point-Slope Form - This is a practice worksheet for writing linear equations in slope-intercept form using the Converting Linear Equations between Standard Form and Slope-Intercept Form: (allows students to practice writing an equation for a line of fit given a scatter pot.
This worksheet gives students equations written in standard form that. S Point-slope form: write an equation from a graph S Slopes of parallel and perpendicular lines S Write an equation for a parallel or perpendicular line.
EQUATIONS OF LINES IN SLOPE-INTERCEPT AND STANDARD FORM In Section you learned that the graph of all solutions to a linear equation in two variables is a straight line. In this section we start with a line or a description of a line and write an equation for the line.
The equation of a line in any form is called a linear equation in two.