The equation of line s is y = -1/9x - 4. Line t includes the point (1,7) and is perpendicular to line s. What is the equation of line t? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers. ______

Question

The equation of line s is y = -1/9x - 4. Line t includes the point (1,7) and is perpendicular to line s. What is the equation of line t? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.   ______

Bytelearn · Accepted Answer

Determine slope of line s: Determine the slope of line s. The equation of line s is given as y = -1/9x - 4. The slope (m) of a line in the slope-intercept form y = mx + b is the coefficient of x. Therefore, the slope of line s is -1/9.Find slope of line t: Find the slope of line t. Since line t is perpendicular to line s, its slope will be the negative reciprocal of the slope of line s. The negative reciprocal of -1/9 is 9 (because -1/(-1/9) = 9). Therefore, the slope of line t is 9.Use point-slope form: Use the point-slope form to find the equation of line t. We have the slope of line t (m = 9) and a point on line t (1,7). The point-slope form of a line is y - y1 = m(x - x1), where (x1, y1) is a point on the line. Plugging in the values, we get y - 7 = 9(x - 1).Simplify equation to slope-intercept form: Simplify the equation to slope-intercept form. To get the slope-intercept form y = mx + b, we distribute the slope on the right side and add 7 to both sides: y - 7 = 9x - 9. Adding 7 to both sides gives us y = 9x - 9 + 7, which simplifies to y = 9x - 2.

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