Which of the following equations represents a line that passes through the points (4,-8) and (0,-5) ? I. 3x+4y=-20 II. y+2=-(3)/(4)(x+4) Neither I only II only I and II

Find Slope: Find the slope of the line passing through the points (4,-8) and (0,-5). The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1). m = (-5 - (-8)) / (0 - 4) m = (3) / (-4) m = -3/4Write Point-Slope Equation: Use the slope and one of the points to write the equation of the line in point-slope form. Let's use the point (4, -8) and the slope -3/4. The point-slope form is y - y1 = m(x - x1). y - (-8) = (-3/4)(x - 4) y + 8 = (-3/4)(x - 4)Convert to Slope-Intercept: Convert the point-slope form to slope-intercept form (y = mx + b) to find the y-intercept (b). y + 8 = (-3/4)(x - 4) y = (-3/4)x + 3 + 8 y = (-3/4)x + 11Check Equation I: Check if equation I (3x + 4y = -20) is the same line by rearranging it into slope-intercept form. 3x + 4y = -20 4y = -3x - 20 y = (-3/4)x - 5Check Equation II: Compare the slope and y-intercept of equation I with the line's slope and y-intercept from Step 3. The slope of equation I is -3/4, which matches the slope we found. The y-intercept of equation I is -5, which does not match the y-intercept we found (+11). Therefore, equation I does not represent the line passing through the points (4,-8) and (0,-5).Check if equation II (y + 2 = -(3/4)(x + 4)) is the same line by rearranging it into slope-intercept form. y + 2 = -(3/4)(x + 4) y = -(3/4)x - 3 - 2 y = -(3/4)x - 5Compare the slope and y-intercept of equation II with the line's slope and y-intercept from Step 3. The slope of equation II is -3/4, which matches the slope we found. The y-intercept of equation II is -5, which does not match the y-intercept we found (+11). Therefore, equation II does not represent the line passing through the points (4,-8) and (0,-5).

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Which of the following equations represents a line that passes through the points
(4,-8) and
(0,-5) ?
I.
3x+4y=-20
II.
y+2=-(3)/(4)(x+4)
Neither
I only
II only
I and II

Which of the following equations represents a line that passes through the points $(4,-8)$ and $(0,-5)$ ? $\newline$ I. $3 x+4 y=-20$ $\newline$ II. $y+2=-\frac{3}{4}(x+4)$ $\newline$ Neither $\newline$ I only $\newline$ II only $\newline$ I and II

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Math Problems

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

(4,-8)

and

(0,-5)

\newline

3 x+4 y=-20

\newline

II.

y+2=-\frac{3}{4}(x+4)

\newline

Neither

\newline

I only

\newline

II only

\newline

I and II

Find Slope: Find the slope of the line passing through the points $(4,-8)$ and $(0,-5)$ . The slope $m$ is calculated using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ . $m = \frac{-5 - (-8)}{0 - 4}$ $m = \frac{3}{-4}$ $m = -\frac{3}{4}$
Write Point-Slope Equation: Use the slope and one of the points to write the equation of the line in point-slope form. $\newline$ Let's use the point $(4, -8)$ and the slope $-\frac{3}{4}$ . $\newline$ The point-slope form is $y - y_1 = m(x - x_1)$ . $\newline$ $y - (-8) = (-\frac{3}{4})(x - 4)$ $\newline$ $y + 8 = (-\frac{3}{4})(x - 4)$
Convert to Slope-Intercept: Convert the point-slope form to slope-intercept form $y = mx + b$ to find the y-intercept $b$ . $\newline$ $y + 8 = \left(-\frac{3}{4}\right)(x - 4)$ $\newline$ $y = \left(-\frac{3}{4}\right)x + 3 + 8$ $\newline$ $y = \left(-\frac{3}{4}\right)x + 11$
Check Equation I: Check if equation I $3x + 4y = -20$ is the same line by rearranging it into slope-intercept form. $3x + 4y = -20$ $4y = -3x - 20$ $y = \left(-\frac{3}{4}\right)x - 5$
Check Equation II: Compare the slope and y-intercept of equation I with the line's slope and y-intercept from Step $3$ . $\newline$ The slope of equation I is $-\frac{3}{4}$ , which matches the slope we found. $\newline$ The y-intercept of equation I is $-5$ , which does not match the y-intercept we found ( $+11$ ). $\newline$ Therefore, equation I does not represent the line passing through the points $(4,-8)$ and $(0,-5)$ .
Check Equation II: Compare the slope and $y$ -intercept of equation I with the line's slope and $y$ -intercept from Step $3$ . $\newline$ The slope of equation I is $-\frac{3}{4}$ , which matches the slope we found. $\newline$ The $y$ -intercept of equation I is $-5$ , which does not match the $y$ -intercept we found ( $+11$ ). $\newline$ Therefore, equation I does not represent the line passing through the points $(4,-8)$ and $(0,-5)$ .Check if equation II ( $y + 2 = -\left(\frac{3}{4}\right)(x + 4)$ ) is the same line by rearranging it into slope-intercept form. $\newline$ $y + 2 = -\left(\frac{3}{4}\right)(x + 4)$ $\newline$ $y$ $1$ $\newline$ $y$ $2$
Check Equation II: Compare the slope and y-intercept of equation I with the line's slope and y-intercept from Step $3$ . $\newline$ The slope of equation I is $-\frac{3}{4}$ , which matches the slope we found. $\newline$ The y-intercept of equation I is $-5$ , which does not match the y-intercept we found ( $+11$ ). $\newline$ Therefore, equation I does not represent the line passing through the points $(4,-8)$ and $(0,-5)$ .Check if equation II ( $y + 2 = -\left(\frac{3}{4}\right)(x + 4)$ ) is the same line by rearranging it into slope-intercept form. $\newline$ $y + 2 = -\left(\frac{3}{4}\right)(x + 4)$ $\newline$ $y = -\left(\frac{3}{4}\right)x - 3 - 2$ $\newline$ $y = -\left(\frac{3}{4}\right)x - 5$ Compare the slope and y-intercept of equation II with the line's slope and y-intercept from Step $3$ . $\newline$ The slope of equation II is $-\frac{3}{4}$ , which matches the slope we found. $\newline$ The y-intercept of equation II is $-5$ , which does not match the y-intercept we found ( $+11$ ). $\newline$ Therefore, equation II does not represent the line passing through the points $(4,-8)$ and $(0,-5)$ .