Question

i need help with this explain what the "y-intercept" and "slope" of a two variable linear equation are. How can you find the y-intercept and slope given a linear equation? How would this change if you were given the graph of the linear equation instead of the equation itself? How could you find the slope if you were given two points, but neither the graph nor the equation? show a linear equation

Answer 1

Alright lets start with the first part of your question, which is: explain what the "y-intercept" and "slope" of a two variable linear equation are.

So The y-intercept is the point where the line crosses the y axis
The slope describes how steep the line is.

Answer 2

for question two. How can you find the y-intercept and slope given a linear equation?
For the next part, often we're given equations in the form y = mx + b
Does that look at all familiar? @sharon248

Answer 3

In that equation, m is the slope
and b is the y-intercept
So the slope is whatever number is in front of the x in the line equation
and the y-intercept is whatever number is all by itself in the equation

Answer 4

Ok, now lets look at question 3: How would this change if you were given the graph of the linear equation instead of the equation itself?
I'll draw an example line for us to look at...

Answer 5

If we were given this equation, we could look at the number markings along the y axis to see the number where it crosses that axis (the y-intercept)
For example, if it crosses at the third number marking, the y intercept is 3
Then to get the slope, we also need the x-intercept first
Then the slope is the y intercept divided by the x intercept
Or more specifically, the change in y divided by change in x between those two points
Between those two points, the line goes up 3 units, and to the right 3
So our slope is 3/3
= 1

Answer 6

Alright, lets move on to question 4 now. How could you find the slope if you were given two points, but neither the graph nor the equation?

Answer 7

For this one first I'll write the general slope formula for two points, then we can look at an example with numbers. First let's say the two points are (x1, y1) and (x2, y2)