Which of the following equations represents a line that passes through the points (0,5) and (6,-3) ? I. 4x+3y=12 II. y=-(4)/(3)x+7 Neither I only II only I and II

Calculate Slope: Find the slope of the line passing through the points (0,5) and (6,-3). The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1). Here, (x1, y1) = (0, 5) and (x2, y2) = (6, -3). m = (-3 - 5) / (6 - 0) = -8 / 6 = -4 / 3.Write Point-Slope Equation: Use the slope and one of the points to write the equation of the line in point-slope form. We can use the point (0,5) and the slope -4/3. The point-slope form is y - y1 = m(x - x1). Substituting the values, we get y - 5 = (-4/3)(x - 0).Convert to Slope-Intercept Form: Convert the point-slope form to slope-intercept form (y = mx + b). y - 5 = (-4/3)x + 0 Add 5 to both sides to solve for y. y = (-4/3)x + 5.Check Equation I: Check if equation I (4x + 3y = 12) is the same line. To check, we need to convert this equation to slope-intercept form. 3y = -4x + 12 y = (-4/3)x + 4. This is not the same as y = (-4/3)x + 5, so equation I does not represent the line passing through the points (0,5) and (6,-3).Check Equation II: Check if equation II (y = -(4/3)x + 7) is the same line. Compare this equation with the one we derived (y = (-4/3)x + 5). The slopes are the same, but the y-intercepts are different (7 vs. 5). Therefore, equation II also does not represent the line passing through the points (0,5) and (6,-3).

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Which of the following equations represents a line that passes through the points
(0,5) and
(6,-3) ?
I.
4x+3y=12
II.
y=-(4)/(3)x+7
Neither
I only
II only
I and II

Which of the following equations represents a line that passes through the points $(0,5)$ and $(6,-3)$ ? $\newline$ I. $4 x+3 y=12$ $\newline$ II. $y=-\frac{4}{3} x+7$ $\newline$ Neither $\newline$ I only $\newline$ II only $\newline$ I and II

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Algebra 2

Write a quadratic function from its x-intercepts and another point

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Q. Which of the following equations represents a line that passes through the points

(0,5)

and

(6,-3)

\newline

4 x+3 y=12

\newline

II.

y=-\frac{4}{3} x+7

\newline

Neither

\newline

I only

\newline

II only

\newline

I and II

Calculate Slope: Find the slope of the line passing through the points $(0,5)$ and $(6,-3)$ . The slope $m$ is calculated using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ . Here, $(x_1, y_1) = (0, 5)$ and $(x_2, y_2) = (6, -3)$ . $m = \frac{-3 - 5}{6 - 0} = \frac{-8}{6} = \frac{-4}{3}$ .
Write Point-Slope Equation: Use the slope and one of the points to write the equation of the line in point-slope form. $\newline$ We can use the point $(0,5)$ and the slope $-\frac{4}{3}$ . $\newline$ The point-slope form is $y - y_1 = m(x - x_1)$ . $\newline$ Substituting the values, we get $y - 5 = (-\frac{4}{3})(x - 0)$ .
Convert to Slope-Intercept Form: Convert the point-slope form to slope-intercept form $y = mx + b$ . $\newline$ $y - 5 = \left(-\frac{4}{3}\right)x + 0$ $\newline$ Add $5$ to both sides to solve for $y$ . $\newline$ $y = \left(-\frac{4}{3}\right)x + 5$ .
Check Equation I: Check if equation I $4x + 3y = 12$ is the same line. $\newline$ To check, we need to convert this equation to slope-intercept form. $\newline$ $3y = -4x + 12$ $\newline$ $y = \left(-\frac{4}{3}\right)x + 4$ . $\newline$ This is not the same as $y = \left(-\frac{4}{3}\right)x + 5$ , so equation I does not represent the line passing through the points $(0,5)$ and $(6,-3)$ .
Check Equation II: Check if equation II $y = -\left(\frac{4}{3}\right)x + 7$ is the same line. $\newline$ Compare this equation with the one we derived $y = \left(-\frac{4}{3}\right)x + 5$ . $\newline$ The slopes are the same, but the y-intercepts are different $7$ vs. $5$ . $\newline$ Therefore, equation II also does not represent the line passing through the points $(0,5)$ and $(6,-3)$ .