Math 154 Elementary Algebra. Equations of Lines 4.4
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1 Math Elementary Algebra Caspers Name Date Equations of Lines. For each graph, solve each equation for y (if necessary), then write down the slope and y-intercept.. y x. y x Equation solved for y: Equation solved for y: m: y-intercept: m: y-intercept: Slope-Intercept Form If an equation of a line is solved for y, and therefore in the form y mx b, the slope of the line is the coefficient of x or m, and the y-value of the y-intercept is b. Not all equations of lines are written in this form; however you can solve any equation for y and get it in this form. y mx b is called the slope-intercept form of an equation of a line because the slope and the y-value of the y-intercept is readily seen. Determine the slope and the y-intercept of the line represented by the given equation.. y x. x y For problems through, determine the slope and y-intercept of the line represented by each equation. Graph the line using the slope and y-intercept.. y x. x y Equation solved for y: Equation solved for y: m: y-intercept: m: y-intercept: Page of
2 . y x. y x Equation solved for y: Equation solved for y: m: y-intercept: m: y-intercept: Parallel and Perpendicular Lines The slopes of two parallel lines are the same, and the slopes of two perpendicular lines are opposite reciprocals. The slope-intercept form of an equation of a line, y mx b, is very useful for determining the slope of the line, m, and the y-intercept of the line,,b. This information may be used to graph the line, or to figure out if two lines are parallel, perpendicular or neither. Without graphing, determine whether each pair of lines is parallel, perpendicular or neither. 9. x y y x. x y x y Equation solved for y: Equation solved for y: m : m : Equation solved for y: Equation solved for y: m : m : Page of
3 . x y x 9 y. x y x y Equation solved for y: Equation solved for y: m : m : Equation solved for y: Equation solved for y: m : m : Point Slope Form If an equation of a line is in the form y y m x x, the slope of the line is m, and, on the line. Any point (one at a time) can be used for, x y is a point x y. Notice that there are minus signs built into the formula. Usually equations that are given are not written in this form; however, this form is very useful for writing an equation of a line. For each equation, write down the slope and the point on the line that can be read directly from the equation.. y x m:, x y =. y x m:, x y =. y x m:, x y = Page of
4 Writing Equations of Lines Understanding the slope-intercept form of an equation of a line, y mx b, and the point-slope form of an equation of a line y y m x x, not only allows a line to be easily graphed from an equation, it also gives a way to write an equation of a slanted line given either the graph or other information. If the y-intercept is given, use slope-intercept form:. Write down slope-intercept form: y mx b. Find the m -value, which is the slope of the line. Make sure to take the rise over the run, or the change in y over the change in x! The slope may be stated in the problem. You may have to find the slope graphically. You may have to find it by using two points that are given in the formula m y y. x x You may have to use the fact that parallel lines have the same slope. You may have to use the fact that perpendicular lines have slopes that are the negative reciprocal of each other.. Find the b-value, which is the y-value of the y-intercept,bof the line. The y-intercept,b may be stated in the problem. You may have to find it graphically; it is the point where the line crosses the y-axis. You may have to use a point-slope equation first (see below) then solve that equation for y.. Plug in the m-value and the b-value into y mx b. Don t forget the x! If the y-intercept is NOT given, use point-slope form first: y y m x x. Write down point-slope form:. Find the m-value, which is the slope of the line. The slope may be stated in the problem. You may have to find the slope graphically. You may have to find it by using two points that are given in the formula m y y. x x You may have to use the fact that parallel lines have the same slope. You may have to use the fact that perpendicular lines have slopes that are the negative reciprocal of each other.. Use a point given in the problem as the point, x y.. Plug in the m-value and the point x, y into y y m x x. Watch out for negatives and subtraction signs! Page of
5 Equations of Horizontal and Vertical Lines If the line is horizontal, use y "t he y-value of the y-i nt ercept ". If the line is vertical, use x "t he x-value of the x-i nt ercept " Determine the equation of each line m: m: y-intercept: y-intercept: m: m: y-intercept: x-intercept: y-intercept: x-intercept: Page of
6 Write the equation of the line, with the given properties, in slope-intercept form.. Slope =, through,. Slope = through,. Slope = through,. Through, and,.. Through, and,.. Parallel to y x and through,. Perpendicular to y x and through, Page of
3.5 Day 1 Warm Up. Graph each line. 3.4 Proofs with Perpendicular Lines
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