Question

What is the equation of this line in standard form? 6x−7y=−11 6x−7y=11 6x−5y=−13 7x−6y=11 Number graph ranging from negative five to five on the x and y axes. A line is drawn on the graph that passes through the labeled points begin ordered pair negative three comma negative one end ordered pair and begin ordered pair one-half comma two end ordered pair

Answer 1

The equation of the line in standard form is 6x - 7y = -11.

Explanation:

To find the equation of the line, we can use the point-slope form of linear equations. The point-slope form is:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is a point on the line.

We are given that the line passes through the points (-3, -1) and (1/2, 2). Let's use these points to find the slope of the line.

m = (y2 - y1)/(x2 - x1) = (2 - (-1))/(1/2 - (-3)) = 3/4

Now that we know the slope of the line, we can plug it into the point-slope form of the equation. We will use the point (-3, -1) as our point on the line.

y - (-1) = 3/4 * (x - (-3))

y + 1 = 3/4 * x + 2.25

y = 3/4 * x - 1.25

We can simplify this equation to 6x - 7y = -11.