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6 Graph a bine that has a slope of
-(3)/(4) and inclubes the point
(-3,2)

$6$ Graph a bine that has a slope of $-\frac{3}{4}$ and inclubes the point $(-3,2)$

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Write a polynomial from its roots

Full solution

Q.

6

Graph a bine that has a slope of

-\frac{3}{4}

and inclubes the point

(-3,2)

Use Slope-Intercept Form: First, we need to use the slope-intercept form of a line, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
Calculate Equation with Slope: Since we know the slope $m$ is $-\frac{3}{4}$ , we can start with $y = -\frac{3}{4}x + b$ .
Find Y-Intercept: Now we need to find the y-intercept $b$ using the point $(-3,2)$ that the line passes through. We plug these values into the equation: $2 = -\left(\frac{3}{4}\right)(-3) + b$ .
Solve for Y-Intercept: Solving for $b$ , we get $2 = \frac{9}{4} + b$ . To find $b$ , we subtract $\frac{9}{4}$ from both sides: $2 - \frac{9}{4} = b$ .
Final Equation of Line: Converting $2$ to $\frac{8}{4}$ to subtract, we get $\frac{8}{4} - \frac{9}{4} = b$ , which simplifies to $b = -\frac{1}{4}$ .
Graph Y-Intercept: Now we have the full equation of the line: $y = -\left(\frac{3}{4}\right)x - \frac{1}{4}$ .
Use Slope to Find Point: To graph the line, we start at the y-intercept (0, -rac{1}{4}) and use the slope to find another point. From (0, -rac{1}{4}), we go down $3$ units and right $4$ units to plot a second point.
Draw Line Through Points: Draw a straight line through the two points to complete the graph of the line.

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