Unit 4 Linear Equations Test Study Guide

Linear Equations

• A linear equation with a slope of 1 and a y-intercept of -7 is represented by the equation y = x - 7
• The slope and y-intercept of the equation 2x + 5y = 20 can be found by rewriting it in slope-intercept form (y = mx + b), giving a slope of -2/5 and a y-intercept of 4

Graphing Lines

• The equation of a line graphed can be written in slope-intercept form (y = mx + b) or point-slope form (y - y1 = m(x - x1)) given the graph

Intercepts

• The x-intercept of the equation 4x - y = 4 is the point where the line intersects the x-axis, found by setting y = 0 and solving for x

Horizontal Lines

• A horizontal line has a slope of 0 and can be represented by the equation y = k, where k is the y-intercept

Parallel and Perpendicular Lines

• The slope-intercept form of a line parallel to the line 5x – 2y = 18 and passing through the point (-2, -1) can be found by first rewriting the original equation in slope-intercept form and then using the same slope and the given point
• The equation of a line perpendicular to the line y = -3x + 2 has a slope that is the negative reciprocal of -3
• The equation of a line parallel to y = -4x + 5 and passing through the point (-2, -1) has the same slope as the original line
• The equation of a line perpendicular to 3x – 5y = 5 and passing through the point (9, -14) has a slope that is the negative reciprocal of the slope of the original line

Applications of Linear Equations

• The line of best fit can be used to predict the number of students enrolled in Beach Manor Preschool in 2010
• The line of best fit can be used to estimate Luke’s golf score for week 12
• Linear equations can be used to solve real-world problems, such as finding the number of prints MaryAnn can order from an online print shop given a budget of $35
• Linear equations can be used to solve real-world problems, such as finding the cost of renting a boat from Smith Mountain Lake Boat Rentals for the Jones Family
• Linear equations can be used to solve real-world problems, such as finding the number of wreaths Alaina sold if she sold 15 poinsettias and made $543

Prepare for your Unit 4 Linear Equations test with this study guide, covering topics such as slope, slope-intercept form, and standard form of linear equations. Practice writing linear equations, identifying slopes and y-intercepts, and more.