Which of the following equations represents a line that passes through the points (-5,9) and (5,3) ? I. 3x+5y=25 II. y=-(3)/(5)x+6 Neither I only II only I and II

Calculate Slope: First, we need to find the slope of the line that passes through the points (-5,9) and (5,3). The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.Use Point-Slope Form: Using the points (-5,9) and (5,3), we calculate the slope as follows: m = (3 - 9) / (5 - (-5)) = (-6) / (10) = -3/5.Convert to Slope-Intercept Form: Now that we have the slope, we can use the point-slope form of the equation of a line, y - y1 = m(x - x1), to find the equation of the line. We can use either of the two points for this; let's use the point (-5,9).Check Equation I: Substituting the slope and the point (-5,9) into the point-slope form, we get: y - 9 = (-3/5)(x - (-5)) y - 9 = (-3/5)(x + 5)Check Equation II: Now we simplify the equation and put it in slope-intercept form (y = mx + b): y = (-3/5)x - (3/5)(5) + 9 y = (-3/5)x - 3 + 9 y = (-3/5)x + 6Identify Correct Answer: We have found the equation of the line in slope-intercept form to be y = (-3/5)x + 6. Now we need to check which of the given equations matches this equation.Let's check equation I: 3x + 5y = 25. To see if this is equivalent to our equation, we need to solve for y in terms of x. 5y = -3x + 25 y = (-3/5)x + 5 This equation is not the same as y = (-3/5)x + 6, so equation I does not represent the line that passes through the points (-5,9) and (5,3).Now let's check equation II: y = -(3/5)x + 6. This equation is exactly the same as the one we derived, y = (-3/5)x + 6. Therefore, equation II does represent the line that passes through the points (-5,9) and (5,3).Since only equation II matches our derived equation, the correct answer is ＂II only＂.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which of the following equations represents a line that passes through the points
(-5,9) and
(5,3) ?
I.
3x+5y=25
II.
y=-(3)/(5)x+6
Neither
I only
II only
I and II

Which of the following equations represents a line that passes through the points $(-5,9)$ and $(5,3)$ ? $\newline$ I. $3 x+5 y=25$ $\newline$ II. $y=-\frac{3}{5} x+6$ $\newline$ Neither $\newline$ I only $\newline$ II only $\newline$ I and II

View step-by-step help

Home

Math Problems

Algebra 2

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

Full solution

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

(-5,9)

and

(5,3)

\newline

3 x+5 y=25

\newline

II.

y=-\frac{3}{5} x+6

\newline

Neither

\newline

I only

\newline

II only

\newline

I and II

Calculate Slope: First, we need to find the slope of the line that passes through the points $(-5,9)$ and $(5,3)$ . The slope $m$ is calculated 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.
Use Point-Slope Form: Using the points $(-5,9)$ and $(5,3)$ , we calculate the slope as follows: $\newline$ $m = \frac{3 - 9}{5 - (-5)} = \frac{-6}{10} = -\frac{3}{5}.$
Convert to Slope-Intercept Form: Now that we have the slope, we can use the point-slope form of the equation of a line, $y - y_1 = m(x - x_1)$ , to find the equation of the line. We can use either of the two points for this; let's use the point $(-5,9)$ .
Check Equation I: Substituting the slope and the point $(-5,9)$ into the point-slope form, we get: $\newline$ $y - 9 = \left(-\frac{3}{5}\right)(x - (-5))$ $\newline$ $y - 9 = \left(-\frac{3}{5}\right)(x + 5)$
Check Equation II: Now we simplify the equation and put it in slope-intercept form $y = mx + b$ :
$y = \left(-\frac{3}{5}\right)x - \left(\frac{3}{5}\right)(5) + 9$
$y = \left(-\frac{3}{5}\right)x - 3 + 9$
$y = \left(-\frac{3}{5}\right)x + 6$
Identify Correct Answer: We have found the equation of the line in slope-intercept form to be $y = \frac{-3}{5}x + 6$ . Now we need to check which of the given equations matches this equation.
Identify Correct Answer: We have found the equation of the line in slope-intercept form to be $y = \frac{-3}{5}x + 6$ . Now we need to check which of the given equations matches this equation.Let's check equation I: $3x + 5y = 25$ . To see if this is equivalent to our equation, we need to solve for $y$ in terms of $x$ . $5y = -3x + 25$ $y = \frac{-3}{5}x + 5$ This equation is not the same as $y = \frac{-3}{5}x + 6$ , so equation I does not represent the line that passes through the points $(-5,9)$ and $(5,3)$ .
Identify Correct Answer: We have found the equation of the line in slope-intercept form to be $y = \frac{-3}{5}x + 6$ . Now we need to check which of the given equations matches this equation.Let's check equation I: $3x + 5y = 25$ . To see if this is equivalent to our equation, we need to solve for $y$ in terms of $x$ . $5y = -3x + 25$ $y = \frac{-3}{5}x + 5$ This equation is not the same as $y = \frac{-3}{5}x + 6$ , so equation I does not represent the line that passes through the points $(-5,9)$ and $(5,3)$ .Now let's check equation II: $y = -\frac{3}{5}x + 6$ . This equation is exactly the same as the one we derived, $y = \frac{-3}{5}x + 6$ . Therefore, equation II does represent the line that passes through the points $(-5,9)$ and $(5,3)$ .
Identify Correct Answer: We have found the equation of the line in slope-intercept form to be $y = \frac{-3}{5}x + 6$ . Now we need to check which of the given equations matches this equation.Let's check equation I: $3x + 5y = 25$ . To see if this is equivalent to our equation, we need to solve for $y$ in terms of $x$ . $5y = -3x + 25$ $y = \frac{-3}{5}x + 5$ This equation is not the same as $y = \frac{-3}{5}x + 6$ , so equation I does not represent the line that passes through the points $(-5,9)$ and $(5,3)$ .Now let's check equation II: $y = -\frac{3}{5}x + 6$ . This equation is exactly the same as the one we derived, $y = \frac{-3}{5}x + 6$ . Therefore, equation II does represent the line that passes through the points $(-5,9)$ and $(5,3)$ .Since only equation II matches our derived equation, the correct answer is ＂II only＂.