Question

Write an equation for the line described. Give the answer in standard form.

Through (6,5), m= -8. The equation of the line is :
(Type your answer in standard form.) a) y=−8x+53
b) y=−8x−47
c) y=8x−47
d) y=8x+53

Answer 1

To write the equation of the line with a slope of -8 passing through the point (6,5), we use the slope-intercept form y = mx + b to first find the y-intercept b. With the slope m as -8 and b found to be 53, the slope-intercept equation becomes y = -8x + 53. Rewriting this in standard form, we get 8x + y = 53.

Step-by-step explanation:

To write the equation for a line given a point (6,5) through which it passes and a slope m of -8, we start with the slope-intercept form of a line equation, which is y = mx + b. Here, m is the slope and b is the y-intercept. Plugging in the given point and the slope into the equation, we get:

5 = (-8)(6) + b

Which simplifies to:

5 = -48 + b

Adding 48 to both sides to solve for b, we find:

b = 53

Substituting the values for m and b back into the slope-intercept form yields:

y = -8x + 53

But we want the standard form, which is Ax + By = C. By rewriting our equation, we get:

8x + y = 53

This is the standard form of the equation of the line.