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Progetto CLIL - Liceo Scientifico “N. Copernico” – a. s. 2016-2017 prof. Silvia Valente Linear equations Exercises 1) Classify each of the following as true or false: a. (-1,-6) is a solution of 4x-y=2. b. 3x-y=4 and y=3x-4 are equivalent. c. The abscissa of (2, -5) is -5. d. The graph of 2x-3y=6 is a line, for all real numbers x and y. e. The point with coordinates (1,-2) is on the graph of 3x-2y=1. f. The graph of x=0 is the y-axis. g. y=6x-1 is a linear equation in implicit form. h. The equation of the horizontal line passing through (3,-2) is x=-2 i. The graph of x+y=3 crosses the x-axis at (0,3). j. The graph of y=4 is a vertical line. 2) Complete the gaps in the sentences below with the correct word or phrase from the box: y-intercept straight line rise fall horizontal y explicit slope 0 y-intercept slope m The measure of steepness of a line is called The letter … … is used to denote slope. Lines with positive slopes … from left to right. Lines with negative slopes … from left to right. … All points whose y coordinates are 2 lie on a If the x coordinate is 0, then the point lies on the line. … axis. In the equation y=mx+q, m represents the … of the line. In the equation y=mx+q, q represents the … of the line. The equation y=mx+q is called the … form of a linear equation. The y-coordinate at which a line crosses the y axis is called the You can find the y-intercept of a line by replacing x with The graph of y=mx+q is a … … … File3 Progetto CLIL - Liceo Scientifico “N. Copernico” – a. s. 2016-2017 prof. Silvia Valente 3) Fill in In the coordinate plane, the graph of y=mx+q is a … If you want to graph a straight line, you need … points The equation of the straight line that passes through the points A(4,-1) and B(8,-1) is … The slope of y=9x-2 is … and its intercept on the y-axis is … y=-4 represents a … line. … The point (3,9) belongs to the straight line y= 5x-6 because its coordinates The equation of the y-axis is … The equation of a line parallel to the x-axis is … The straight lines y=4x-3 and y= 4x are … because … x=2 is parallel to the … axis. The straight lines y=x + 3 and y= -6x+3 pass both through … … because Exercises. 4) What is the equation of a line with slope -2 and y-intercept 0? … 5) Find the slope of each line whose equation is given: 2x+y-8=0 3x-4y-1=0 6) Write an equation in standard form of the line that has the given slope and y-intercept: m=-2, q=5; m=-4/5, q=-5 7) Change each equation to the slope-intercept (=explicit) form. Then draw the graph of each on your exercise book: x-y-3=0 x+2y=0 9x-3y-4=0 3 8) What is the slope of all lines parallel to y x ? … 4 9) Which point is not on the line 2x+3y=12 ? (0,4) (6,0) (3,2) (2,3) 10) What is the equation of a line with slope -2 and which passes through the point (3,-1)? y=-2x-1 y=-2x+5 y=-2x+3 y=5x-2 11) Which of the following is the equation of a line with -3 as its y intercept and parallel to 2 the line y x 3 ? 3 2 2 2 3 y 3x y x3 y x 3 y x 3 3 3 3 2 File3