Find an equation of the line $L$ that passes through the point $(- 6, 4)$ and satisfies the condition. (Let $x$ be the independent variable and $y$ be the dependent variable.)
$L$ passes through the point $(2, \frac{7}{2})$ .

Answer

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Finally, the equation of the line $L$ that passes through the point $(- 6, 4)$ and $(2, \frac{7}{2})$ is $y = \frac{1}{16} x + \frac{35}{8}$ .

Steps

Step 1 ：First, we can find the slope of the line through these two points. The slope will be equal to: $\frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{\frac{7}{2} - 4}{2 - (- 6)} = \frac{\frac{1}{2}}{8} = \frac{1}{16}$

Step 2 ：Therefore, the line will have the form $y = \frac{1}{16} x + b$ . To solve for $b$ , substitute in one of the given points for $x$ and $y$ as shown: $\begin{aligned} 4 & = \frac{1}{16} (- 6) + b \\ \Rightarrow 4 & = - \frac{3}{8} + b \\ \Rightarrow \frac{35}{8} & = b \end{aligned}$

Step 3 ：Since $b$ in a line of the form $y = m x + b$ is the $y$ -intercept, and this is what we are trying to find, the answer is $\frac{35}{8}$ .

Step 4 ：Finally, the equation of the line $L$ that passes through the point $(- 6, 4)$ and $(2, \frac{7}{2})$ is $y = \frac{1}{16} x + \frac{35}{8}$ .

Find an equation of the line L that passes through the point (−6,4) and satisfies the condition. (Let x be the independent variable and y be the dependent variable.)L passes through the point (2,72).

Answer

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Find an equation of the line $L$ that passes through the point $(- 6, 4)$ and satisfies the condition. (Let $x$ be the independent variable and $y$ be the dependent variable.)
$L$ passes through the point $(2, \frac{7}{2})$ .