Question

1. What Is The Equation Of The Line, In Slope-Intercept Form, That Passes Through (3, -1) And (-1, 5)?

Figuring out the equation of a line that passes through two points can be a tricky endeavor for beginner algebra students. However, with some practice and understanding of the slope-intercept form, it’s easy to figure out the equation of any line. In this article, we’ll take a look at what the equation of the line is in slope-intercept form that passes through two given points, (3, -1) and (-1, 5). We’ll go over how to calculate the slope and y-intercept before providing an example problem to help you understand the concepts.

What is the equation of a line?

In order to find the equation of a line, one must first determine the slope. The slope is the ratio of the rise to the run, or in other words, the change in y over the change in x. In this case, the rise is -2 and the run is 3, so the slope is -2/3. To find the equation of a line in slope-intercept form, one must first solve for y. This can be done byplugging in one of the points given, (0,-6) for example, and solving for y. This will give you y=-2/3x-6. Now that you have solved for y, all you have to do is plug your slope (-2/3) and one of your points (0,-6) into the equation y=-2/3x+b and solve for b. This will give you b=-6. So now your equation should look like this: y=-2/3x-6

What is slope-intercept form?

Slope-intercept form is a way to express the equation of a line in mathematical terms. It is written as y = mx + b, where m is the slope of the line and b is the y-intercept. The slope is the number that tells us how steep the line is, and the y-intercept is the point where the line crosses the y-axis.

How to find the equation of a line in slope-intercept form

There are a few steps to finding the equation of a line in slope-intercept form:
First, identify the slope of the line. This can be done by finding the rise (the difference in y-values) and run (the difference in x-values) between two points on the line. The slope is equal to the rise over the run, or m=y2−y1x2−x1.
Once the slope is found, use one of the points on the line and the slope to find the y-intercept. This is done by plugging in the values for x and y into y=mx+b and solving for b.
Now that both the slope and y-intercept are known, they can be plugged into the equation y=mx+b to find the equation of the line in slope-intercept form.

The equation of the line that passes through (3, -1) and (-1, 5)

The equation of the line that passes through (3, -1) and (-1, 5) is y = 2x + 4.

How to use the equation to find points on the line

To find points on the line using the equation, plug in the values for x and y into the equation. For example, if you want to find out what the coordinates are for the point where x=1, you would plug in 1 for x and solve for y. This would give you the coordinate (1,2) since y=2 when x=1. You can use this method to find any point on the line.

Conclusion

To conclude, the equation of the line in slope-intercept form that passes through the points (3,-1) and (-1,5) is y = 4x + 7. This equation can be used to calculate x and y values for any point on this particular line. Additionally, it can help us determine whether two lines are parallel or perpendicular to one another. With this equation, you will have all of the important information you need to work with equations involving lines in your future endeavors!

2. Have you ever been given a question in math class that left you scratching your head wondering, “What is the equation of the line, in slope-intercept form, that passes through (3, -1) and (-1, 5)?”

Slope-intercept form is an equation of a line in the form of y = mx + b, where m is the slope and b is the y-intercept. Using this form, we can easily find the equation of a line that passes through two given points.

Let’s first look at what we know. We know that the line passes through the two points (3, -1) and (-1, 5). In order to find the equation of the line, we will need to calculate the slope.

The slope is the rate at which y changes in relation to x. To calculate the slope, we can use the formula m = (y2 – y1) / (x2 – x1). In this case, we are given the two points (3, -1) and (-1, 5) so we would use the following formula: m = (5 – (-1)) / (-1 – 3). After plugging in our values and simplifying, we get: m = -6/4 or m = -3/2.

Now that we have our slope, we can move on to finding the y-intercept. The y-intercept is the point at which the line crosses the y-axis. To find the y-intercept, we can plug our slope into the equation y = mx + b and solve for b.

Let’s use our slope, -3/2, and the point (3, -1). We can substitute in our values and solve for b by rearranging the equation to get b = -7/2.

We now have all the information we need to write the equation of the line in slope-intercept form. Our slope is -3/2 and our y-intercept is -7/2. Therefore, the equation of the line in slope-intercept form that passes through (3, -1) and (-1, 5) is y = -3/2x – 7/2.