Which of the following equations represents a line that passes through the points (0,7) and (-9,10) ? I. 2x+6y=42 II. y=-(1)/(3)x+7 Neither I only II only I and II

Question

Which of the following equations represents a line that passes through the points  (0,7) and  (-9,10) ? I.  2x+6y=42 II.  y=-(1)/(3)x+7 Neither I only II only I and II

Bytelearn · Accepted Answer

Calculate Slope: First, we need to determine the slope of the line that passes through the points (0,7) and (-9,10). The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).Find Y-Intercept: Using the points (0,7) as (x1,y1) and (-9,10) as (x2,y2), we calculate the slope as follows: m = (10 - 7) / (-9 - 0) = 3 / -9 = -1/3.Write Equation: Now that we have the slope, we can use one of the points to find the y-intercept (b) of the line. We can use the point (0,7) because it gives us the y-intercept directly since the x-coordinate is 0. Therefore, b = 7.Check Equation I: With the slope m = -1/3 and y-intercept b = 7, the equation of the line in slope-intercept form is y = mx + b, which gives us y = -1/3x + 7.Check Equation II: Now let's check if equation I, 2x + 6y = 42, represents the line. To do this, we can rearrange the equation into slope-intercept form (y = mx + b) by solving for y: 6y = -2x + 42 y = -1/3x + 7.We see that equation I, when simplified, matches the equation y = -1/3x + 7, which we derived from the points. Therefore, equation I represents the line that passes through the points (0,7) and (-9,10).Next, we check equation II, y = -1/3x + 7, which is already in slope-intercept form. This equation matches the one we derived from the points, so equation II also represents the line that passes through the points (0,7) and (-9,10).

Which of the following equations represents a line that passes through the points $(0,7)$ and $(-9,10)$ ? $\newline$ I. $2 x+6 y=42$ $\newline$ II. $y=-\frac{1}{3} x+7$ $\newline$ Neither $\newline$ I only $\newline$ II only $\newline$ I and II

Full solution

More problems from Write a linear equation from two points

Related topics

Which of the following equations represents a line that passes through the points (0,7) (0,7) (0,7) and (−9,10) (-9,10) (−9,10) ?\newlineI. 2x+6y=42 2 x+6 y=42 2x+6y=42\newlineII. y=−13x+7 y=-\frac{1}{3} x+7 y=−31​x+7\newlineNeither\newlineI only\newlineII only\newlineI and II

Which of the following equations represents a line that passes through the points $(0,7)$ and $(-9,10)$ ? $\newline$ I. $2 x+6 y=42$ $\newline$ II. $y=-\frac{1}{3} x+7$ $\newline$ Neither $\newline$ I only $\newline$ II only $\newline$ I and II