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Find the equations of the lines using the points given
7)
(-1,-4)(3,-3)

Find the equations of the lines using the points given $\newline$ $7$ ) $(-1,-4)(3,-3)$

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Roots of rational numbers

Full solution

Q. Find the equations of the lines using the points given

\newline

7

)

(-1,-4)(3,-3)

Calculate Slope: To find the equation of a line, we need to determine the slope $m$ of the line using the slope formula, which is $m = \frac{y_2 - y_1}{x_2 - x_1}$ , where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points. $\newline$ Let's calculate the slope using the points $(-1, -4)$ and $(3, -3)$ . $\newline$ $m = \frac{-3 - (-4)}{3 - (-1)}$ $\newline$ $m = \frac{-3 + 4}{3 + 1}$ $\newline$ $m = \frac{1}{4}$
Use Point-Slope Form: Now that we have the slope, we can use the point-slope form of the equation of a line, which is $y - y_1 = m(x - x_1)$ , where $m$ is the slope and $(x_1, y_1)$ is a point on the line. $\newline$ Let's use the point $(-1, -4)$ and the slope $\frac{1}{4}$ to write the equation. $\newline$ $y - (-4) = \left(\frac{1}{4}\right)(x - (-1))$ $\newline$ $y + 4 = \left(\frac{1}{4}\right)(x + 1)$
Convert to Slope-Intercept Form: To write the equation in slope-intercept form $y = mx + b$ , we need to distribute the slope $\frac{1}{4}$ across the terms in the parentheses and then isolate $y$ . $\newline$ $y + 4 = \left(\frac{1}{4}\right)x + \left(\frac{1}{4}\right)(1)$ $\newline$ $y + 4 = \left(\frac{1}{4}\right)x + \frac{1}{4}$
Isolate y: Subtract $4$ from both sides to solve for y. $\newline$ $y = (\frac{1}{4})x + \frac{1}{4} - 4$ $\newline$ $y = (\frac{1}{4})x - \frac{15}{4}$

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