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# How do you graph the line with slope $- 1/2$ passing through point $( - 3, - 5)$ ?

Last updated date: 23rd Feb 2024
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Hint: First we will start by forming the equation using the information which is the slope of the equation and a point. Here, we are using the slope point form of line which is given by $y = mx + c$. Then finally graph the equation of the line.

Complete step by step solution:
Generally, there are infinitely many such linear equations. Now we know that the slope point form of line is $y = mx + c$ where $m$ is the slope of the line.
$m = - 1/2 \\ \Rightarrow x = - 3 \\ \Rightarrow y = - 5 \\$
Now, we substitute all these values in the equation $y = mx + c$.
$y = mx + c \\ \Rightarrow - 5 = \left( {\dfrac{{ - 1}}{2}} \right)( - 3) + c \\$
Now, we will simplify the equation further by cross multiplying the terms.
$- 5 = \left( {\dfrac{{ - 1}}{2}} \right)( - 3) + c \\ \Rightarrow - 10 = 3 + 2c \\$
Now take all the like terms to one side.
$- 10 = 3 + 2c \\ \Rightarrow - 10 - 3 = 2c \\$
Now we will solve for the value of $c$ that is the y-intercept.
$- 10 - 3 = 2c \\ \Rightarrow - 13 = 2c \\ \Rightarrow c = \dfrac{{ - 13}}{2} \\$
Hence, the value of y-intercept is $\dfrac{{ - 13}}{2}$. Now we will solve for the value of x-intercept by substituting $y = 0$ in the slope point form of line.
$y = mx + c \\ \Rightarrow 0 = \left( {\dfrac{{ - 1}}{2}} \right)(x) - \dfrac{{13}}{2} \\ \Rightarrow\dfrac{{13}}{2} = \left( {\dfrac{{ - 1}}{2}} \right)x \\ \Rightarrow 13 = - x \\ \therefore x = 13 \\$
Hence, the value of x-intercept is $- 13$. Now we know the y-intercept, x-intercept, slope of the line and the point through which the line passes hence, we will plot the graph.