Complete the equation of the line through (3,-1) and (4,7). Use exact numbers. 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 = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) 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). m = (7 - (-1)) / (4 - 3) m = (7 + 1) / (1) m = 8 / 1 m = 8Using 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 - y1 = m(x - x1), where m is the slope and (x1, y1) 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 - 24Converting 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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Math Problems

Algebra 2

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 $y$ . $y = 8x - 24 - 1$ $y = 8x - 25$