# Chapter 1, Equations and Graphs - Section 1.3 - Lines - 1.3 Exercises - Page 113: 68

x-intercept = 7 y-intercept = -6 Refer to the image below for the graph.

#### Work Step by Step

Write the equation in $Ax +By=C$ form. This will make solving for the intercepts a lot easier. The given equation can be rewritten as: $6x-7y-42=0 \\6x-7y-42+42=0+42 \\6x-7y=42$ To find the $x$ intercept, set $y=0$ then solve for $x$ to obtain: $6x-7y=42 \\6x-7(0) = 42 \\6x=42 \\\dfrac{6x}{6}=\dfrac{42}{6} \\x=7$ The x-intercept is $7$. To find the $y$ intercept, set $x=0$ then solve for $y$ to obtain: $6x-7y=42 \\6(0)-7y = 42 \\-7y=42 \\\dfrac{-7y}{-7}=\dfrac{42}{-7} \\y=-6$ The y-intercept is $-6$. To draw the graph of the equation, plot the x-intercept point $(7, 0)$ and the y-intercept point $(0, -6)$ and connect them using a straight line. (refer to the attached image in the answer part above)

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