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## Find the x and y intercepts

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**Find the x and y intercepts**• How do you find the slope of a line using the x and y intercept? SPI: 706.3.8**x- and y-Intercepts**• The graphical concept of x- and y-intercepts is pretty simple. The x-intercepts are where the graph crosses the x-axis, and the y-intercepts are where the graph crosses the y-axis. • The problems start when we try to deal with intercepts algebraically.**To clarify the algebraic part, think again about the axes.**When you were first introduced to the Cartesian plane, you were shown the regular number line from elementary school (the x-axis), and then shown how you could draw a perpendicular number line (the y-axis) through the zero point on the first number line. Take a closer look, and you'll see that the y-axis is also the line "x = 0". In the same way, the x-axis is also the line "y = 0".**Then, algebraically,**• an x-intercept is a point on the graph where y is zero • a y-intercept is a point on the graph where x is zero.**More specifically,**• an x-intercept is a point in the equation where the y-value is zero, and • a y-intercept is a point in the equation where the x-value is zero.**The x-intercept of a line is the point at which the line**crosses the x axis. ( i.e. where the y value equals 0 )x-intercept = ( x, 0 )The y-intercept of a line is the point at which the line crosses the y axis. ( i.e. where the x value equals 0 )y-intercept = ( 0, y )**Find the x and y intercepts of the equation 3x + 4y = 12.**• To find the x-intercept, set y = 0 and solve for x. • 3x + 4( 0 ) = 12 3x + 0 = 12 3x = 12x = 12/3x = 4**Find the x and y intercepts of the equation 3x + 4y = 12.**• To find the x-intercept, set y = 0 and solve for x. • 3x + 4( 0 ) = 12 3x + 0 = 12 3x = 12x = 12/3x = 4**Find the x and y intercepts of the equation 3x + 4y = 12.**• To find the y-intercept, set x = 0 and solve for y. • 3( 0 ) + 4y = 12 0 + 4y = 12 4y = 12y = 12/4y = 3**Find the x and y intercepts of the equation 3x + 4y = 12.**• To find the y-intercept, set x = 0 and solve for y. • 3( 0 ) + 4y = 12 0 + 4y = 12 4y = 12y = 12/4y = 3**Writing the Ordered Pair for the x and y intercepts**• Once you have solved for both the x and y, you write your answers as ordered pairs. • So your x is going to be what you solved x to be and 0, because that is what you substituted for y in the equation. • Same thing for the y ordered pair: it is going to be 0 plus what you solved y to be.**Therefore, the x-intercept is ( 4, 0 ) and the y-interceptis**( 0, 3 ). • The graph of the line looks like this:**Find the x and y intercepts of the equation 2x - 3y = -6.**• To find the x-intercept, set y = 0 and solve for x. • 2x - 3( 0 ) = -6 2x - 0 = -6 2x = -6x = -6/2x = -3 • To find the y-intercept, set x = 0 and solve for y. • 2( 0 ) - 3y = -6 0 - 3y = -6 -3y = -6y = -6/(-3)y = 2**Therefore, the x-intercept is ( -3, 0 ) and the**y-interceptis ( 0, 2 ). • The graph of the line looks like this:**Find the x and y intercepts of the equation ( -3/4 )x + 12y**= 9. • To find the x-intercept, set y = 0 and solve for x. • ( -3/4 )x + 12( 0 ) = 9 ( -3/4 )x + 0 = 9 ( -3/4 )x = 9x = 9/( -3/4 )x = -12 • To find the y-intercept, set x = 0 and solve for y. • ( -3/4 )( 0 ) + 12y = 9 0 + 12y = 9 12y = 9y = 9/12y = 3/4**Therefore, the x-intercept is ( -12, 0 ) and the**y-intercept is ( 0, 3/4 ). • The graph of the line looks like this: