Question

Write the standard form of a line where the slope is 1/2 and a point on the line is (4, -2).

a) 2x - y = 8
b) x - 2y = 8
c) 2x - y = -8
d) x - 2y = -8

Answer 1

To write the standard form of a line with a slope of 1/2 and passing through the point (4, -2), you use the slope-intercept form to find the y-intercept and then rearrange to get the standard form. The correct answer is 'b) x - 2y = 8'.

Step-by-step explanation:

The question asks to write the standard form of a line with a slope of 1/2 passing through the point (4, -2). The standard form of a line is ax + by = c, where a, b, and c are integers. With the slope (m) being 1/2 and using the given point to solve for b (y-intercept), you can use the slope-intercept form y = mx + b to find the equation of the line.

First, plug the slope and the point into the slope-intercept form:

-2 = (1/2)*4 + b

Now, solve for b:

-2 = 2 + b

b = -4

Then, write the slope-intercept form with the slope and b(y-intercept):

y = (1/2)x - 4

To convert this into standard form, multiply through by 2 to avoid fractions:

2y = x - 8

Finally, rearrange to get the standard form:

x - 2y = 8

So, the correct answer is b) x - 2y = 8.