Please help me solve this problem... thanks!

1.Find the equation of the line that cntains the pont (5, -1) and has slope -1/2

2.find the equation of the line that passes through the points (-2,1) and (1,-5)

Easiest way, since you don't specify which form you want your equation in.

(based on the fact that for Ax + By = C 0, the slope is -A/B)

1. Slope = -1/2
so the equation is x + 2y = C
plug in point, 5 - 2 = C
C = 3
so ..... x + 2y = 3

from there you can change it to any form they ask for.

try the second one the same way.

Sure! I can help you solve both problems. Let's start with the first one.

To find the equation of a line, we'll use the point-slope form of a linear equation, which is: y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope.

For the first problem, we're given the point (5, -1) and the slope -1/2. Substituting these values into the point-slope form, we have:

y - (-1) = (-1/2)(x - 5)

Simplifying the equation, we get:

y + 1 = (-1/2)x + 5/2

Finally, let's rearrange the equation to the standard form: Ax + By = C. We'll move all terms to the left-hand side:

(1/2)x + y = 3/2

Therefore, the equation of the line that contains the point (5, -1) and has a slope of -1/2 is (1/2)x + y = 3/2.

Now, let's move on to the second problem.

To find the equation of a line passing through two points (-2, 1) and (1, -5), we'll use the point-slope form or find the slope-intercept form.

First, let's calculate the slope (m) using the formula: m = (y2 - y1) / (x2 - x1). Substituting the given points (-2, 1) and (1, -5), we get:

m = (-5 - 1) / (1 - (-2))
= -6 / 3
= -2

Now that we have the slope, we can use the point-slope form. Let's choose the first point (-2, 1):

y - 1 = -2(x - (-2))
= -2(x + 2)

Simplifying this equation, we get:

y - 1 = -2x - 4

Let's rearrange the equation to the slope-intercept form (y = mx + b), where b is the y-intercept:

y = -2x - 4 + 1
y = -2x - 3

Therefore, the equation of the line passing through the points (-2, 1) and (1, -5) is y = -2x - 3.

I hope this helps! Let me know if you have any further questions.