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All About Linear Equations Things you Need to Know at New Trier 1) Find the equation of the line that has a slope of -4 and a y-intercept of 18. 2) Find the equation of the line that goes through the point (5,6) and has a slope of ½. 3) Find the equation of the line that goes through the points (3,5) and (-4,9). 4) Find the equation of the line that is vertical and passes through (4,-5). 5) Find the equation of the line that is horizontal and passes through (9,-3). 6) Find the x and y intercepts of the line 2x – 3y = 12. Write these answers as two separate coordinates. 7) A line passes through (5,-2) and (4,-4). Write an equation of this line in all three forms (point-slope, slope-intercept, and standard form). a. Point-slope: b. Slope-intercept: c. Standard form: . 8) Find the equation of the line that is parallel to 2x – 6y = 18 and passes through (5,-8). 9) Find the equation of the line that is perpendicular to y = 4x – 3 & passes through (6,-8). Graph each of the following lines: *Hint: You don’t always have to put equations in slope-intercept form in order to graph them. An equation in point-slope form tells you a different point from which to begin using the slope. An equation in standard form make it easy to find the two intercepts. Just graph the two intercepts and then use a ruler to draw the line. ! ! 10) 𝑦 = − ! 𝑥 + 4 11) 𝑦 − 3 = ! (𝑥 − 2) 12) 3𝑥 − 4𝑦 = 12 13) 2𝑦 = −4𝑥 + 10 14) 𝑦 = 4 15) 𝑥 = −2