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Complete the equation of the line through
(3,-1) and
(4,7).
Use exact numbers.

y=

Complete the equation of the line through $(3,-1)$ and $(4,7)$ . $\newline$ Use exact numbers. $\newline$ $y=$

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Find the roots of factored polynomials

Full solution

Q. Complete the equation of the line through

(3,-1)

and

(4,7)

.

\newline

Use exact numbers.

\newline

y=

Finding the Slope: To find the equation of a line, we need to determine the slope ( $m$ ) and the y-intercept ( $b$ ) of the line. The slope can be found using the formula $m = \frac{(y_2 - y_1)}{(x_2 - x_1)}$ , where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points the line passes through.
Calculating the Slope: Let's calculate the slope using the points $(3, -1)$ and $(4, 7)$ . $\newline$ $m = \frac{7 - (-1)}{4 - 3}$ $\newline$ $m = \frac{7 + 1}{1}$ $\newline$ $m = \frac{8}{1}$ $\newline$ $m = 8$
Using Point-Slope Form: Now that we have the slope, we can use point-slope form to write the equation of the line. The point-slope form is $y - y_1 = m(x - x_1)$ , where $m$ is the slope and $(x_1, y_1)$ is a point on the line.
Plugging in Values: Using the point $(3, -1)$ and the slope $m = 8$ , we can plug these into the point-slope form. $y - (-1) = 8(x - 3)$ $y + 1 = 8x - 24$
Converting to Slope-Intercept Form: To get the equation in slope-intercept form $y = mx + b$ , we need to isolate $y$ . $y = 8x - 24 - 1$ $y = 8x - 25$

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