206k views
5 votes
Lines has an equation of y = -9/4x + 4. Perpendicular to lines is line t, which passes through the point (-3, -1). What is the equation of line t? Write the equation in slope-intercept form.

User Emcpadden
by
8.9k points

1 Answer

3 votes

Final answer:

To find the equation of line t, we need to find the slope of the given line and then find its negative reciprocal. Using the point-slope form of a line, we can find the equation of line t by plugging in the values of the point and slope. The equation of line t is y = (4/9)x + 1/3, written in slope-intercept form.

Step-by-step explanation:

To find the equation of line t that is perpendicular to the given line, we need to find the slope of the given line and then find its negative reciprocal. The given line has a slope of -9/4, so the slope of line t will be 4/9.

Using the point (-3, -1) that the line passes through, we can use the point-slope form of a line to find the equation of line t.

The point-slope form is y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Plugging in the values, we have y - (-1) = (4/9)(x - (-3)), which simplifies to y + 1 = (4/9)(x + 3).

Finally, we can rewrite the equation in slope-intercept form by solving for y. Distributing 4/9 to both terms inside the parentheses, we get y + 1 = (4/9)x + 4/3.

Subtracting 1 from both sides, we have y = (4/9)x + 4/3 - 1, which simplifies to y = (4/9)x + 1/3. Therefore, the equation of line t is y = (4/9)x + 1/3, written in slope-intercept form.

User Schalkneethling
by
8.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories