Graphing Lines Practice

1. Graph $y=-\dfrac{4}{3}x+8$.

   
   

2. Graph $y=2x-7$.

   
   

3. Graph $y=-\dfrac{3}{2}x-3$.

   
   

4. Graph $y=-3x+7$.

   
   

Source: Khan Academy, https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8bb11595b61c86:graphing-slope-intercept-equations/e/graph-from-slope-intercept-equation
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1. The equation is in slope-intercept form: $y=m\!\cdot\!x+b$. In this form, $m$ gives us the slope of the line and $b$ gives us its $y$-intercept.

   So $y=-\dfrac{4}{3}x+8$ has a slope of $-\dfrac{4}{3}$ and a $y$-intercept at $(0,8)$.

   We need two points. We already have the $y$-intercept
   $(0,8)$.

   We can find a second point by reasoning about the slope. A slope of $-\dfrac{4 }{3 }$ means that when the $x$-value increases by ${3 }$, the $y$-value decreases by ${4 }$.

   $(0 {+3},8 {-4})=(3,4)$

   
   

   Now we can graph the equation.

   
   

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2. The equation is in slope-intercept form: $y=m\!\cdot\!x+b$. In this form, $m$ gives us the slope of the line and $b$ gives us its $y$-intercept.

   So $y=2x-7$ has a slope of $2$ and a $y$-intercept at
   $(0,-7)$.

   We need two points. We already have the $y$-intercept
   $(0,-7)$.

   We can find a second point by reasoning about the slope. A slope of  $2$ means that when the $x$-value increases by ${1}$, the $y$-value increases by
   ${2}$.

   $(0 {+1},-7 {+2})=(1,-5)$

   
   

   Now we can graph the equation.

   
   

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3. The equation is in slope-intercept form: $y=m\!\cdot\!x+b$. In this form, $m$ gives us the slope of the line and $b$ gives us its $y$-intercept.

   So $y=-\dfrac{3}{2}x-3$ has a slope of $-\dfrac{3}{2}$ and a $y$-intercept at $(0,-3)$.

   We need two points. We already have the $y$-intercept
   $(0,-3)$.

   We can find a second point by reasoning about the slope. A slope of $-\dfrac{3 }{2 }$ means that when the
   $x$-value increases by ${ 2}$, the $y$-value decreases by ${3 }$.

   $(0 {+2},-3 {-3})=(2,-6)$

   
   

   Now we can graph the equation.

   
   

   ---

4. The equation is in slope-intercept form: $y=m\!\cdot\!x+b$. In this form, $m$ gives us the slope of the line and $b$ gives us its $y$-intercept.

   So $y=-3x+7$ has a slope of $-3$ and a $y$-intercept at $(0,7)$.

   We need two points. We already have the $y$-intercept
   $(0,7)$.

   We can find a second point by reasoning about the slope. A slope of $-3$ means that when the $x$-value increases by ${1}$, the $y$-value decreases by ${3}$.

   $(0 {+1},7 {-3})=(1,4)$

   
   

   Now we can graph the equation.