A line passes through the points (-1,6) and (1,-6) . Write its equation in tercept form. Write your an swer using integers , proper fractions, and improper fractions in simplest form. square

To find the equation of a line in intercept form, we need to find the x and y-intercepts of the line. The x-intercept is the point where the line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis.<br /><br />Step 1: Find the slope of the line using the given points.<br />The slope of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:<br />\[m = \frac{y_2 - y_1}{x_2 - x_1}\]<br /><br />Using the given points $(-1,6)$ and $(1,-6)$, we can substitute into the formula to find the slope:<br />\[m = \frac{-6 - 6}{1 - (-1)} = \frac{-12}{2} = -6\]<br /><br />Step 2: Use the slope-intercept form of a linear equation to find the equation of the line.<br />The slope-intercept form of a linear equation is given by:<br />\[y = mx + b\]<br />where m is the slope and b is the y-intercept.<br /><br />We already found the slope to be -6. To find the y-intercept, we can substitute one of the given points into the equation and solve for b. Let's use the point $(-1,6)$:<br />\[6 = -6(-1) + b\]<br />\[6 = 6 + b\]<br />\[b = 0\]<br /><br />So, the equation of the line in slope-intercept form is:<br />\[y = -6x + 0\]<br />or simply:<br />\[y = -6x\]<br /><br />Step 3: Convert the equation to intercept form.<br />The intercept form of a linear equation is given by:<br />\[\frac{x}{a} + \frac{y}{b} = 1\]<br />where (a, 0) and (0, b) are the x and y intercepts respectively.<br /><br />We can find the x-intercept by setting y = 0 in the equation:<br />\[0 = -6x\]<br />\[x = 0\]<br /><br />And the y-intercept is already found to be 0.<br /><br />So, the equation of the line in intercept form is:<br />\[\frac{x}{0} + \frac{y}{0} = 1\]<br /><br />However, since division by zero is undefined, we need to find another way to express the intercept form. Since both intercepts are at the origin (0,0), the intercept form is not applicable here. Instead, we use the point-slope form with the given points:<br /><br />\[y - y_1 = m(x - x_1)\]<br /><br />Using point $(-1,6)$:<br />\[y - 6 = -6(x + 1)\]<br />\[y - 6 = -6x - 6\]<br />\[y = -6x\]<br /><br />Thus, the equation of the line is:<br />\[y = -6x\]<br /><br />Final Answer: The equation of the line in intercept form is not applicable as both intercepts are at the origin. Instead, the equation of the line is:<br />\[y = -6x\]