Two-variable equations: Quiz $3$ $\newline$ Graph $y=-\frac{3}{2} x-3$ . $\newline$ Check

Full solution

Q. Two-variable equations: Quiz

3

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Graph

y=-\frac{3}{2} x-3

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Check

Plot y-intercept: Plot the y-intercept on the graph. $\newline$ The y-intercept is where $x=0$ , so plug $x=0$ into the equation to find $y$ . $\newline$ $y = -\left(\frac{3}{2}\right)(0) - 3$ $\newline$ $y = -3$ $\newline$ So the y-intercept is $(0, -3)$ .
Find slope: Find the slope of the line. $\newline$ The slope is the coefficient of $x$ , which is $-\left(\frac{3}{2}\right)$ . $\newline$ This means for every $2$ units we move to the right (positive $x$ direction), we move $3$ units down (negative $y$ direction) because the slope is negative.
Plot another point: Plot another point using the slope. $\newline$ Starting from the y-intercept $(0, -3)$ , move $2$ units to the right and $3$ units down. $\newline$ This gives us the point $(2, -6)$ . $\newline$ Plot the point $(2, -6)$ on the graph.
Draw the line: Draw the line through the points $(0, -3)$ and $(2, -6)$ . Use a ruler to make sure the line is straight.
Check line: Check if the line is correct. $\newline$ Choose a point not already used, like $(4, -9)$ . $\newline$ Plug $x=4$ into the equation to see if $y$ equals $-9$ . $\newline$ $y = -\left(\frac{3}{2}\right)(4) - 3$ $\newline$ $y = -6 - 3$ $\newline$ $y = -9$ $\newline$ The point $(4, -9)$ lies on the line, so the graph is correct.